Tri 10.5
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10.5 Mixed application problems
To solve application problems involving trigonometry: • Draw a diagram and label the key information. • Identify and draw the appropriate right-angled triangles separately. • Solve using trigonometry to find the missing measurements. • Express your answer in words.
Example A parasail company guarantees that each customer will reach a height of 32 metres. If the rope is attached to the boat at a point 1 metre above the waterline and it makes an angle of 35º to the horizontal, what is the length of rope?
Solution Draw the triangle, labelling all relevant information, including the unknown length.
x 32m 31m 35°
1m
31m is opposite the given angle. x is the hypotenuse. So sine is the appropriate ratio.
sin 35o
31 x
xsin 35° = 31
x
31 sin 35o = 54.05m, correct to 2 decimal places
Ex 10E
To solve application problems involving trigonometry: • Draw a diagram and label the key information. • Identify and draw the appropriate right-angled triangles separately. • Solve using trigonometry to find the missing measurements. • Express your answer in words.
Example A parasail company guarantees that each customer will reach a height of 32 metres. If the rope is attached to the boat at a point 1 metre above the waterline and it makes an angle of 35º to the horizontal, what is the length of rope?
Solution Draw the triangle, labelling all relevant information, including the unknown length.
x 32m 31m 35°
1m
31m is opposite the given angle. x is the hypotenuse. So sine is the appropriate ratio.
sin 35o
31 x
xsin 35° = 31
x
31 sin 35o = 54.05m, correct to 2 decimal places
Ex 10E
