The angle of elevation of the top of a tower as observed from a point on the ground isα and - Maths - Some Applications of Trigonometry

Question

The angle of elevation of the top of a tower as observed from a
point on the ground isα and on moving 'a' metre
towards the tower the angle of elevation isβ Prove that
the height of the tower is
a tanα tanβ
tanβ- tanα

Ankush Jain · Accepted Answer

Let h m be the height of tower Given DC = a m and BC = x m

In âˆ†ABC $\tan β = \frac{h}{x} \Rightarrow x = \frac{h}{\tan β} (1)$ In âˆ†ABD, we have $\tan α = \frac{h}{a + x} \Rightarrow \tan α = \frac{h}{a + \frac{h}{\tan β}} [using (1)] \Rightarrow \tan α = \frac{h \tan β}{a \tan β + h}$ â‡’ a tan Î² tan Î± + h tan Î± = h tan Î² â‡’ h (tan Î² â€“ tan Î±) = a tan Î² tan Î± $\Rightarrow h = \frac{a \tan β \tan α}{\tan β - \tan α}$

The angle of elevation of the top of a tower as observed from a point on the ground isα and on moving 'a' metre towards the tower the angle of elevation isβ.Prove that the height of the tower is a tanα.tanβ tanβ- tanα

The angle of elevation of the top of a tower as observed from a point on the ground isα and on moving 'a' metre towards the tower the angle of elevation isβ.Prove that the height of the tower is

a tanα.tanβ

tanβ- tanα