The angle of elevation of the top of the tower as observed from a point on the ground…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The angle of elevation of the top of the tower as observed from a point on the ground is

\alpha

and on moving 'a' metres towards the tower, the angle of elevation becomes

\beta

. Prove that the height of the tower is

\frac{a\tan\alpha \tan\beta}{\tan\beta - \tan\alpha}