# Inverse Trigonometry Exploration

Author:
Ben Graber
Trigonometry can be used not only to find the measurements of side lengths, but the measurements of angles. Given the values of trigonometric ratios for different reference angles, it is possible to calculate the ratio for a triangle and use the ratio to find a reference angle. Calculate the side length ratios of the triangles below and use this to find the angles of the triangles. Sin 25° = 0.4226 Sin 30° = 0.5000 Sin 35° = 0.5736 Sin 40° = 0.6429 Sin 45° = 0.7071 Sin 50° = 0.7660 Sin 55° = 0.8192 Sin 60° = 0.8660 Sin 65° = 0.9063
a. Consider the triangle ABC. Calculate the sine ratio of angle A. What is the value of opp/hyp? Which of the sine ratios given above does this equal? What is the measurement of angle A? b. Calculate the sine ratio of angle C. What is the value of opp/hyp? Which of the sine ratios given above does this equal? What is the measurement of angle C? c. Consider the triangle DEF. Calculate the sine ratio of angle D. What is the value of opp/hyp? Which of the sine ratios given above does this equal? What is the measurement of angle D? What is the angle measurement of angle F? d. Consider the triangle HGK. Calculate the sine ratio of angle H. What is the value of opp/hyp? Which of the sine ratios given above does this equal? What is the measurement of angle H? What is the angle measurement of angle K? e. Consider the triangle IJL. Calculate the sine ratio of angle I. What is the value of opp/hyp? Which of the sine ratios given above does this equal? What is the measurement of angle I? What is the angle measurement of angle L?