An observer at point P on level ground finds that the angle of elevation of the top…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry
Problem
An observer at point P on level ground finds that the angle of elevation of the top of a vertical tower is α. After moving d metres straight towards the foot of the tower to point Q, the angle of elevation becomes β (β>α).
Carry out the tasks given below:
(a) Draw a clearly labelled diagram representing the above situation and, from it, write algebraic expressions for the height of the tower in terms of α,β, and the unknown horizontal distances.
(b) Hence prove that the height h of the tower is given by
h=tanβ−tanαdtanαtanβ.