Trigonometry Problems

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MSTE-Trigonometry and Surveying 16. If sin  = k, which of the following is not correct:

Find the length of hypotenuse c if a = 12 and b = 9. A. 13 B. 14 C. 15 D. 16

A. cos  =

One side of a rectangle, inscribed in a circle of diameter 17 cm is 8 cm. Find the area of the rectangle. A. 136 cm² B. 120 cm² C. 142 cm² D. 150 cm²

1 − k2

B. sec  = 1/

k2 − 1

C. tan  = k/ 1 − k 2 D. csc  = 1/k

17. If cos  = 1/3t, find cot . A.

In a right triangle, the hypotenuse has length 20 and the ratio of the two arms is 3:4. Find the longer arm. A. 12 B. 14 C. 15 D. 16

9t 2 − 1

B. 1/ 9t 2 − 1 C.

1 − 9t 2

D. 1/ 1 − 9t 2

18. Solve the right triangle ABC in which A = 35°10’ and c = 72.5. A. a = 59.3; b = 41.8 C. a = 48.1; b = 53.9 B. a = 41.8; b = 59.3 D. a = 53.9; b = 48.1

Find the length of the altitude to the base of an isosceles triangle if the base is 8 and the equal sides are 12. A. 6√2 B. 8√2 C. 10√2 D. 12√2

19. Solve for x from the following equation: sin(2x + 15) = All units are in degrees. A. 37.5 B. 17.5

The sides of a right triangle are in arithmetic progression whose common difference if 6 cm. its area is: A. 216 cm2 C. 360 cm2 B. 270 cm2 D. 144 cm2

C. 22.5

1 . sec(4x − 60)

D. 27.5

20. Find the value of x such that the tangent of angle (2x + 18) is equal to the cotangent of the angle (4x - 12). A. 16 B. 15 C. 13 D. 14

Find the distance d from the center of a circle of radius 17 to a chord whose length is 30. A. 6 B. 7 C. 8 D. 9

21. The base of an isosceles triangle is 20.4 cm and the base angles are 48°40’. Find the equal sides of the triangle. A. 16.7 cm B. 14.2 cm C. 15.4 cm D. 11.6 cm

Find the length of a common external tangent to two externally tangent circles with radii 4 and 9. A. 12.5 B. 11.5 C. 12 D. 13

22. A ladder leans against the side of a building with its foot 12 ft from the building. How far from the ground is the top of the ladder and how long is the ladder if it makes an angle of 70° with the ground? A. 45 ft B. 38 ft C. 42 ft D. 35 ft

A 50-foot supporting wire is to be attached to a 75-foot antenna. Because of surrounding buildings, sidewalks, and roadways, the wire must be anchored exactly 20 feet from the base of the antenna. How high from the base of the antenna is the wire attached? A. 11√22 B. 11√21 C. 10√22 D. 10√21

23. A tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50° with the ground and the top of the tree is now 20 ft from its base, how tall was the tree? A. 61 ft B. 49 ft C. 42 ft D. 55 ft

A wire is needed to support a vertical pole 15 feet tall. The cable will be anchored into a stake 8 feet from the base of the pole. How much cable is needed? A. 19.2 feet B. 20 feet C. 17 feet D. 22.5 feet

24. To find the width of a river, a surveyor set up his surveying equipment at C on one bank and sighted across to a point B on the opposite bank; then, turning through an angle of 90°, he laid off a distance CA = 225 m. Finally, setting the equipment at A, he measured ∠CAB as 48°20’. Find the width of the river. A. 325 m B. 235 m C. 253 m D. 352 m

10. A man cycles 24 km due south and then 20 km due east. Another man, starting at the same time as the first man, cycles 32 km due east and then 7 km due south. Find the distance between the two men. A. 21.69 km B. 17.65 km C. 23.45 km D. 20.81 km

25. When supporting a pole is fastened to it 20 feet from the ground 15 feet from the pole. Determine the angle it makes with the pole. A. 53.13° B. 36.87° C. 53.13° D. 36.87°

11. A spider and a fly are located at opposite vertices of a room of dimensions 1, 2, and 3 units. Assuming that the fly is too terrified to move, find the minimum distance the spider must crawl to reach the fly. A. √14 units B. √18 units C. √20 units D. √26 units

26. A rectangle is 48 cm long and 34 cm wide. What is the angle the diagonal makes with the longer side? A. 38° B. 35° C. 30° D. 27°

12. In a room, 40 feet long, 20 feet wide, and 20 feet high, a bug sits on an end wall at a point one foot from the other floor, midway between the sidewalls. He decides to go on a journey to a point on the other end wall which is one foot from the ceiling midway between the sidewalls. Having no wings, the bug must make his trip by sticking to the surfaces of the room. What is the shortest route that the bug can take? A. 40 B. 46 C. 58 D. 62

27. A tree 100 ft tall casts a shadow 120 ft long. Find the angle of elevation of the sun. A. 40° B. 35° C. 45° D. 30°

13. What is the longest 6’-wide shuffle board court which will fit in a 20’ × 30’ rectangular room? A. 30 7/8 ft B. 28 7/8 C. 29 7/8 D. 27 7/8

29. Find the height of a tree if the angle of elevation of its top changes from 20° to 40° as the observer advances 75 ft toward its base. A. 46.2 ft B. 41.6 ft C. 48.2 ft D. 58.5 ft

14. An isosceles right triangle ABC has its right angle at B. A point inside the triangle is 4 m from A, 3 m from B and 5 m from C. Determine its hypotenuse AC. A. 8.6 m B. 6.1 m C. 9.4 m D. 12.3 m

30. A tower cast a 49-meter shadow when the angle of elevation of the sun is 54. How long will its shadow be when the angle of elevation of the sun is 32? A. 84.35 m B. 121.87 m C. 95.46 m D. 107.93 m

15. A and B live at two opposite corners of a square lot. C and D live at the other two corners. They all carry water from a spring located within the lot, which is 5 rods from A; 4 rods from B; 3 rods from C. How far must D carry water? A. 4.243 rods B. 5.657 rods C. 4.432 rods D. 5.576 rods

31. From point A on level ground, the angles of elevation of the top D and bottom B of a flagpole situated on the top of a hill are measured as 47° 54’ and 39° 45’. Find the height of the hill if the height of the flagpole is 115.5 ft. A. 334.28 B. 349.28 C. 394.28 D. 344.28

28. From the top of a lighthouse 120 m above the sea, the angle of depression of a boat is 15°. How far is the boat from the lighthouse? A. 455 m B. 448 m C. 460 m D. 472 m

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GERTC – November 2018

MSTE-Trigonometry and Surveying

32. Two buildings with flat roofs are 60 m apart. From the roof of the shorter building, 40 m in height, the angle of elevation to the edge of the roof of the taller building is 40. How high is the taller building? A. 90 m B. 95 m C. 86 m D. 84 m 33. A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower? A. 76.31 m B. 73.31 m C. 73.16 m D. 73.61 m

44. Solve the triangle ABC, given a = 38.1, A = 46.5°, and C = 74.3°. Which of the following gives the length of side b. A. 42.6 B. 51.6 C. 48.6 D. 57.6 45. Solve the triangle ABC, given b = 282.7, A = 111.72°, and C = 24.43°. Determine the perimeter of the triangle. A. 830.6 B. 835.1 C. 871.1 D. 866.6 46. Solve the triangle ABC, given b = 67.25, c = 56.92, and B = 65.27°. Determine the measure of angle C. A. 125.75° B. 50.25° C. 61.52° D. 81.22° 47. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° from the vertical directly towards the sun, determine the length of the pole. A. 54.23 m B. 48.23 m C. 42.44 m D. 46.21 m

34. A flagpole stands on the edge of the top of a building. At a point 200 m from the building the angles of elevation of the top and bottom of the pole are 32 and 30 respectively. Calculate the height of the flagpole. A. 6.40 m B. 12.3 m C. 9.50 m D. 16.72 m 35. From a window of a building 4.25 m above the ground, the angle of elevation of the top of a nearby building is 36.6 and the angle of depression of its base is 26.2. What is the height of the nearby building? A. 12.672 m B. 10.665 m C. 11.373 m D. 10.582 m

48. Solve the triangle ABC, given b = 472.1, c = 607.4, A = 125.23°. Solve for a. A. 960.5 B. 950.6 C. 940.30 D. 930.40

36. A man standing on a 48.5 meter building high, has an eyesight height of 1.5 m from the top of the building, took a depression reading from the top of another nearby building and nearest wall, which are 50° and 80° respectively. Find the height of the nearby building in meters. The man is standing at the edge of the building and both buildings lie on the same horizontal plane. A. 39.49 B. 35.50 C. 30.74 D. 42.55

49. Solve the triangle ABC, given a= 322, c = 212, and B = 110°50’. Which of the following gives the measure of angle C? A. 36° 20’ B. 42° 40’ C. 26° 30’ D. 32° 50’

37. A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13° and 35° respectively. The height of the tower is 50 m. Find the height of the monument. A. 29.13 m B. 30.11 m C. 32.12 m D. 33.51 m

51. Solve the triangle ABC, given a = 643.8, b = 778.7, and c = 912.3. Determine the measure of angle A. A. 56.96° B. 43.88° C. 49.11° D. 52.55°

50. Solve the triangle ABC, given a = 25.2, b = 37.8, and c = 43.4. Which of the following gives the measure of angle B? A. 35° 20’ B. 60° 10’ C. 84° 30’ D. 42° 16’

52. A and B are two points on opposite banks of a river. From A, a line AC = 275 m is laid off, and the angles CAB = 125°40’ and ACB = 48°50’ are measured. Find the length of AB. A. 2360 m B. 2510 m C. 2220 m D. 2160 m

38. Two stations A and B were setup to determine the height of a mountain. The angles of elevation to the top of the mountain measured from stations A and B were 27.25 and 30.21, respectively. Station A is 55 m above station B. Station B is 310 m closer to the mountain. If the elevation of station A is 421.63 m, what is the elevation of the top of the mountain? A. 2154.87 m B. 2226.15 m C. 2368.74 m D. 2663.54 m

53. Find the area of triangle ABC, given c = 23 cm, A = 20°, and C = 15°. A. 180 cm2 B. 200 cm2 C. 220 cm2 D. 240 cm2 54. Find the area of triangle ABC, given c = 23 cm, A = 20°, and B = 15°. A. 41 cm2 B. 45 cm2 C. 50 cm2 D. 54 cm2

39. From the top of a lighthouse, 175 ft above the water, the angle of depression of a boat due south is 18°50’. Calculate the speed of the boat if, after it moves due west for 2 min, the angle of depression is 14°20’. A. 234 ft/min B. 222 ft/min C. 227 ft/min D. 244 ft/min

55. Find the area in square units of the triangle ABC, given A = 37°10’, C = 62° 30’, and b = 34.9. A. 331 B. 269 C. 412 D. 205 56. Find the area of triangle ABC, given a = 112 m, b = 219 m, and A = 20°. A. 10,080 m2 B. 6700 m2 C. 8100 m2 D. 4600 m2

40. From the top of a building 100 m high, the angle of depression of a point A due East of it is 30°. From a point B due South of the building, the angle of elevation of the top is 60°. Find the distance AB. A. 100 + 3√30 C. 100 (√30) / 3 B. 200 – √30 D. 100√3/ 30

57. Find the area of triangle ABC, given A = 41°50’, a = 123 ft, and b = 96.2 ft. A. 5100 ft2 B. 5660 ft2 C. 6020 ft2 D. 6620 ft2

41. A clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour hand is 6 inches long. The plane of rotation of the minute hand is 2 inches above the plane of rotation of the hour hand. Find the distance between the tips of the hands at 5:40 AM. A. 9.17 in B. 8.23 in C. 10.65 in D. 11.25 in

58. Three circles with radii 3.0, 5.0, and 9.0 cm are externally tangent. What is the area of the triangle formed by joining their centers? A. 51 cm2 B. 54 cm2 C. 48 cm2 D. 60 cm2 59. The sides of a triangle are a = 23, b = 18, and c = 12. What is the length of the median to side a? A. 15.98 B. 10.09 C. 19.76 D. 13.72

42. A plane hillside is inclined at an angle of 28° with the horizontal. A man wearing skis can climb this hillside by following a straight path inclined at an angle of 12° to the horizontal, but one without skis must follow a path inclined at an angle of only 5° with the horizontal. Find the angle between the directions of the two paths. A. 13.21° B. 18.74° C. 15.56° D. 17.22°

60. What is the radius of the circle circumscribed about a triangle whose sides are 65 in, 78 in, and 92 in, respectively? A. 21.21 in B. 46.78 in C. 34.89 in D. 42.21 in 61. Triangle ABC has sides AB = 45 cm, BC = 32 cm, and AC = 54 cm. How far from side BC is the centroid of the triangle? A. 14.98 cm B. 15.84 cm C. 12.14 cm D. 18.63 cm

43. Solve the triangle ABC, given c = 628, b = 480, and C = 55°10’. Which of the following gives the measure of angle A? A. 68° B. 86° C. 75° D. 57° 2

GERTC – November 2018

MSTE-Trigonometry and Surveying Situation 3 – Complete the data of the given closed traverse. COURSE LENGTH BEARING AB 52.96 N48°20'E BC 59.2 _________ CD 56.36 S7°59'E DE 75.34 _________ EA 42.82 N48°12'W 76.  Compute the bearing of line DE. A. S83°54'W B. S80°3'W C. S82°1'W D. S81°15'W 77.  Compute the bearing of line BC. A. N82°13'E B. N87°33'E C. N84°16'E D. N89°44'E 78.  Determine the area of the lot in square meters. A. 5,225 m2 B. 5,125 m2 C. 5,325 m2 D. 5,425 m2

62. The sides of a triangle ABC are AB = 15 cm, BC = 18 cm, and CA = 24 cm. Determine the distance from the point of intersection of the angular bisectors to side AB. A. 5.21 cm B. 3.78 cm C. 4.73 cm D. 6.25 cm 63. The sides of a triangle ABC are AB = 46 cm, BC = 58 cm, and AC = 68 cm. What is the radius of the inscribed circle, in cm? A. 34.45 B. 18.96 C. 15.31 D. 21.42 64. The sides of a triangle are 18 cm, 23 cm, and 15 cm. What is the length of angle bisector to the 15-cm side? A. 11.78 cm B. 18.94 cm C. 16.36 cm D. 16.83 cm 65. The sides of a triangle are 18 cm, 23 cm, and 15 cm. What is the radius of the inscribed circle, in cm? A. 34.45 B. 18.96 C. 15.31 D. 21.42

Situation 4 – Complete the data of the given closed traverse. Line Length Bearing AB 22 m ___________ BC 25 m S 84° 32' E CD 38 m S 12° 4' W DE ______ S 74° 44' W EA 39 m N 29° 14' W 79.  Determine the length of line DE. A. 16 m B. 18 m C. 20 m D. 22 m 80.  Determine the bearing of line AB A. N 55°56’ E B. N 38°42’ E C. N 62°14' E D. N 70°29’ E 81.  Compute the area of the closed traverse. A. 1228.4 m2 B. 2568.4 m2 C. 1284.2 m2 D. 2456.8 m2

66. The sides of a triangle are 15 in, 18 in, and 23 in. What is the radius of the circumscribing circle, in inches? A. 15.31 B. 34.45 C. 21.42 D. 18.96 67. The sides of a triangle ABC are AB = 46 cm, BC = 58 cm, and AC = 68 cm. What is the radius of the circumscribing circle, in cm? A. 15.31 B. 34.45 C. 21.42 D. 18.96 Surveying (Closed Traverse) 68. A triangular closed traverse has the following data: COURSE AB BC CA

LENGTH 48.65 49.09 ----

Determine the length of the course CA. A. 45.5 m B. 54.4 m C. 56.6 m

BEARING N42°23'E N82°16'W -----

Situation 5 – Complete the data of the given closed traverse. Line 1-2 2-3 3-4 4-5 5-1

D. 65.6 m

69. A closed traverse is given with missing data. Determine the bearing of the course 5-1. COURSE 1-2 2-3 3-4 4-5 5-1

LENGTH 38.4 24.92 43.55 32.91 -----

LINE T-1 T-2 T-3

BEARING N 60 E Due South N 45 W

Compute the area of the triangular lot. A. 51.71 m2 B. 92.25 m2 C. 99.44 m2

D. 73

D. 91 m D. 1.68

DISTANCE 6.0 m 10.0 m 4.0 m D. 66.72 m2

86. A survey set up a transit at point P, which is the inner portion of a four-sided tract of land ABCD, and read the bearings and measures the distances as follows: LINE BEARING DISTANCE PA N 40° 30’ W 504.42 m PB N 38° 00’ E 636.18 m PC S 70° 00’ E 576.9 m PD S 60° 15’ W 834.12 m

Situation 1 –A closed traverse has the following data: LENGTH 179 258.2 --------145.4

D. S73°25’E

85. The transit was set up inside a triangular lot and the bearing and distance of the three corners were observed as follows:

A. N54° 41’E B. N45° 26’E C. N48° 38’E D. N51° 09’E

COURSE AB BC CD DE EA

Bearing N 32° 27' E ___________ S 8° 51' W S 73° 31' W N 18° 44’ W

82.  Compute the bearing of course 2-3. A. S75°35’E B. S71°15’E C. S70°05’E 83.  Compute the length of course 4-5. A. 94 m B. 87 m C. 98 m 84.  Compute the area of the lot in hectares. A. 1.59 B. 1.81 C. 1.72

BEARING S52°51'E S7°53'E S81°42'W N32°50'W ------

70. A closed traverse has the following data: LINE BEARING DISTANCE AB S 15 36’ W 24.22 BC S 69 11’ E 15.92 CD N 57 58’ E --DA S 80 43’ W --Find distance DA in meter. A. 77 B. 75 C. 79

Length 110.8 m 83.6 m 126.9 m ______ 90.2 m

BEARING N47°2'14''E S69°36'4''E S39°35'17''W S87°29'48''W N24°48'09''W

71. Determine the length of course DE. A. 202.40 m B. 183.20 m C. 195.60 m D. 208.50 m 72.  Determine the length of course CD. A. 251.42 m B. 215.35 m C. 202.43 m D.

What is the area of the tract in hectares? A. 45.13 B. 72.2 C. 50.14

D. 60.17

Subdivision of Area 87. A trapezoidal piece of ground is to be divided into two equal parts. The parallel sides are 460 m and 325 m, respectively. The other sides are 130 m and 100 m, If the dividing line is parallel to the parallel sides, determine the length of the dividing line. A. 293.3 B. 398.3 C. 302.3 D. 391.3

Situation 2 – For the given a closed traverse COURSE LENGTH BEARING AB 44.37 S35°30'W BC 137.84 N57°15'W CD 12.83 N1°45'E DE 64.86 -------EA 106.72 -------73.  Determine the bearing of course DE. A. N73°50'E B. N72°10'E C. N70°20'E D. N68°40'E 74.  Determine the bearing of course EA. A. S48°12'E B. S43°52'E C. S46°50'E D. S40°40'E 75.  Determine the area of the closed traverse. A. 5,967 m2 B. 6,597 m2 C. 6,957 m2 D. 5,796 m2

88. A lot is bounded by 3 straight sides namely, AB: N45° E, 160 m long; BC and AC 190 m long in clockwise direction. From point E, 100 m from A and on side AB, a dividing line runs to D which is on side AC. The area of ADE is to be ⅖ of the total area of the lots. The total area of the lot is 11,643.88 m². Compute the distance DE. A. 86.59 m B. 98.65 m C. 89.65 m D. 95.68 m 3

GERTC – November 2018

MSTE-Trigonometry and Surveying

89. Given below is the technical description of a lot, having an area of 640.56 m² It is required to divide this lot into two equal areas such that they will have equal frontage along the line C –D which adjoins a street. Find the direction of this dividing line. lines AB BC CD DE EA

Bearings N 73° 23’ E S 39° 31’ E S 43° 46’ W N 39° 52’W N 15 ° 50’ W

95. Two stations A and B are 540 meters apart. From the following triangulation stations C and D on opposite sides of AB, the following triangulation stations C and D on opposite sides of AB, the following angles were observed. ∠ACD =54° 12’; ∠DCB =41° 24’; ∠ADC =49° 18’; ∠BDC =47° 12’ Find the distance BC to the nearest meter. A. 534 m B. 335 m C. 353 m D. 333 m

Distances 33.46 m 9.21 m 39.27 m 7.06 m 20.50 m

96. A, B and C are three known control stations and P is the position of a sounding vessel which is to be located. If AC = 6925.50 m and AB = 6708.40 m, ∠BAC = 112°45’25”, ∠BPA = 25°32’40”, ∠APC = 45°35’50”, determine the distance AP if A is nearer to P than B and C. A. 4225.32 m B. 4325.23 m C. 4222.35 m D. 4335.43 m

A. N 60°30’W B. N56°35’W C. N55° 31’W D. N 55° 40’ W

97. From two in accessible but intervisible points A and B, the angles to two triangulation stations C and D were observed as follows: Line CD has a distance 500 m. Compute the distance of the line AB. ∠CAB = 79°30’, ∠DAB = 28°30’, ∠DBC = 31°30’, ∠DBA = 84°30’. A. 536.48 m B. 8563.84 m C. 535.68 m D. 538.46 m

90. A parcel of land, with boundaries as described below is to be subdivided into two lots of equal areas. The dividing line is to pass through a point midway between corners A and E, and through a point along the boundary BC. Find the bearing and distance of this dividing line. LINE AB BC CD DE EA

LENGTH 60.00 m 72.69 m 44.83 m 56.45 m 50.00 m

A. N 44°18’E and 79.56 m B. N 45°28’E and 69.34 m

98. In a topographic survey, three triangulation station A, B, and C are sighted from a point P. The distance between the station are AB = 500 m, BC = 350 m, and CA = 540 m at P, the angle subtending AC is 45° while for the azimuth of AC is due North, find the distance PA. A. 415.57 m B. 417.55 m C. 455.71 m D. 451.57 m

BEARING N 15° 30’ E N 82° 23’ E S 17° 20’ E S 70° 36 W N 74° 30’ W

99. In a triangulation surveying station C was due north of A while station D has an azimuth of 223°15’ as observed from A. Station B which is located on the right side of A has a bearing N 81°35’ E, as reckoned from A. The ∠CBD is equal to 29°36’ and ∠CBA is 52°43’. If the distance CD is equal to 250.64 m long, determine the distance between station A and B. A. 300.16 m B. 296.84 m C. 343.64 m D. 289.58 m

C. N 41°17’ E and 75.55 m D. N 42°16’ E and 81.65 m

91. From the data shown below, it is required to divide the lot from a point in line 1-2 of the lot which has a direction of due East which will divide the lot into 2 equal areas. The area of the whole lot is 31,353.91 m². LINES 1-2 2-3 3-4 4-1

BEARING N 31° 49’ E N 86° 30’ E S 22° 10 E N 85° 45’ W

100. A and B are two points located on each bank of a river and near the abutments of a proposed bridge. To determine its distance, a base line CD 180 m long was established on the bank of the river and the transit was set up at stations C and D and the azimuth were taken as follows.

DISTANCES 142.26 160.50 164.99 298.27

LINE C-D C-A C-B D-A D-B

Determine the position of the dividing line from corners 2 and 3. A. 86.61 m and 90.04 m C. 85.79 m and 94.56 m B. 89.73 m and 94.56 m D. 85.65 m and 95.40 m

Compute the length of the line AB. A. 222.34 m B. 221.43 m C. 231.24 m D. 212 .43 m

92. Given below is the technical description of a residential lot. It is required to subdivide the lot into two areas by a line starting from the midpoint of line 1-2 and parallel to line 4-1 .Determine the location of the dividing lined from corner 4 along line 3-4. LINES 1–2 2–3 3–4 4-1 A. 55.28 m

BEARING Due East S 12° 46’ E S 82° 41’W N 14° 05’ E

B. 58.25 m

C. 82.55 m

AZIMUTH 210° 00’ 260° 00’ 290° 00’ 301° 00’ 315° 00’

101. Triangle station A and B were observed from stations 1 and 4 respectively. With the instrument at station 1,the bearing of A was found to be S 70° 30’ E and that of B is S 35° 15’ E .An open traverse is then run from station 1 to 4 where the recorded data as follows LINES BEARINGS DISTANCE 1-2 S 16° 18’ W 120.50 m 2-3 S 13° 22’ E 185.42 m 3-4 S 89° 28’ E 66.46 m With the instrument at station 4, triangulation stations A and B were again observed and A was found to have a bearing of N 15° 20’ E while that of B is N 76°35’ E. It is required to compute for the distance between points A and B. A. 240 m B. 230 m C. 220 m D. 225 m

DISTANCES 101.46 m 53.32 m 131.57 m 70.89 m D. 52.85 m

Triangulation 93. It is desired to determine the distance between two inaccessible objects A and B. Both A and B are visible from two other points C and D, 143.2 meters apart. ∠ADB = 56°32’ and ∠ACB 62°53’. ∠ADB = 88°57’ and horizontal angle between B and D from C is 98° 58’. Determine the distance between A and B. A. 188.72 m B. 174.86 m C. 181.35 m D. 157.27 m

102. A fishing boat left CDO port at 7:00 P.M., the captain received a radio message from the PCG advising him to seek refuge at the nearest island because a typhoon is approaching. At that instant, the captain sighted island of Siquijor and Camiguin and observed the azimuth to be 120° and 308°31’, respectively from his present position. If the boat travels due North of CDO, how far did it travel before the message was received? Coordinates of Camiguin, CDO and Siquijor: NORTHINGS EASTHINGS CAGAYN DE ORO 20000 20000 CAMIGUIN 26250 26085 SIQUIJOR 35600 12195 A. 10931 B. 11930 C. 11093 D. 11039

94. A, C and D are three triangulation shore signals whose positions were determined by the angles ACD = 150° and the sides AC = 850 m and CD = 760 m A sounding at B was taken from a boat and the angles ABC = 42°30’ and CBD = 35°30’ were measured simultaneously by two sextants from the boat to the three shore signals from the shore. Compute the distance BC. A. 1872 m B. 1188 m C. 1286 m D. 1286 m

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