Question

A surveyor want to find out the height of a tower? He measure the angle at A and finds that tana =3/4.what is the height of the tower if A is 30m from its base.

Answer 1

The height of the tower is 22.5 meters.

Step-by-step explanation:

A surveyor measure the angle at A and finds that :

$\tan A=\dfrac{3}{4}$

$A=\tan^{-1}(\dfrac{3}{4})\\\\A=36.86^{\circ}$

It i given that, A is 30 m from its base. We know that,

$\tan A=\dfrac{P}{B}$,  P is perpendicular distance and B is base

Here, P is the height of the tower

$P=B\times \tan A\\\\P=30\times \dfrac{3}{4}\\\\P=22.5\ m$

So, the height of the tower is 22.5 meters.

Learn more,

Trigonometry

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