Sine Exploration Project

Sine Exploration Project Mr. Yates GEOMETRY

Name ________________________ Date ____________ Pd _________

1) Sine of Seventy Degrees a. Draw three RIGHT triangles, each with a 70° angle. Make each one a different size (small, medium, large). b. Measure the sides’ lengths in centimeters. c. Label each side as opposite, adjacent, or hypotenuse, based on the 70° angle. d. For each of your three triangles, calculate the ratio (fraction) opposite .. This ratio is called the sine (of 70°). hypotenuse e. Make sure your calculator is in degree mode. Then find sin 70° with your calculator, by pressing the SIN button, then typing 70. f. Does your answer to part (e) agree with your answers to part (d)? Is it close? 2) Sine of Forty Degrees Repeat steps a-f for three right triangles, each with 40° angles. 3) Sine of Thirty Degrees Repeat steps a-f for three right triangles, each with 30° angles. The triangles you draw should be 30-60-90 special right triangles! 4) Sine of Forty-five Degrees Repeat steps a-f for three right triangles, each with 45° angles. The triangles you draw should be 45-45-90 special right triangles! 5) Sine inverse of 0.8 a. Draw a 3cm,4cm,5cm right triangle, a 6cm,8cm,10cm right triangle, and a 9cm,12cm,15cm right triangle. b. Mark the angle in each triangle opposite the 4, 8, and 12 respectively. c. Label the sides as opposite, adjacent, and hypotenuse. d. Use the definition of sine = opp/hyp to find the sine of the marked angles. e. Use your calculator to find the inverse sine of that number. For example, if your answer to part (d) was 0.2, you would type sin-1(0.2) by pressing 2ND SIN 0.2. f. Measure the marked angles. g. Sine inverse (sin-1) can be used to find an angle if you know its sine ratio. Does your answer to part (e) agree with what you measured in part (f)? 6) Sine inverse of 12/13 Repeat steps a-g for 5,12,13 and 2.5,6,6.5 right triangles, marking the angle opposite the 12 and 6 respectively. 7) Sine inverse of 8/17 Repeat steps a-g for 8,15,17 and 4,7.5,8.5 right triangles, marking the angle opposite the 8 and 4 respectively.