Theory question 104
TrigonometryThe diagram shows a tower TR and an observer at O. |OR| = 84 m and the angle of elevation of the top of the tower T from O is 57°.
(a) Calculate, correct to three significant figures, the height of the tower.
(b) The observer at O, moved away from the tower in the same straight line until the angle of elevation of T is 49°. Find, correct to two decimal places, how far the observer moved backwards.
Show the model answer
Model answer
(a) TR = 84 tan 57° ≈ 129.35 m ≈ 129 m (3 s.f.)
(b) New distance from R = 129.35 ÷ tan 49° ≈ 112.44 m
Distance moved = 112.44 − 84 ≈ 28.44 m
Explanation
Keep the unrounded height for part (b).