Question

The angle of elevation of the top of the tower observed from each of three points A, B, C on the horizontal ground, forming a triangle ABC, is observed to be ${}^{\prime }{\theta }^{\prime }$. If 'R' be the circumradius of the triangle, then height of tower is :

• A. $R\tan \theta$
• B. $R\cot \theta$
• C. $R\sin \theta$
• D. $R\cos \theta$

Answer 1

The correct option is A $R\tan \theta$

Here, Height of tower$=$OD

Circumradius $=OA=OB=OC=R$

We know $:\tan \theta =\frac{opposite}{adjacent}$, so

In triangle OAD, we get

$\tan \left(\alpha OAD\right)=\frac{OD}{OA}$

$\Rightarrow \tan x=\frac{OD}{R}$

$\Rightarrow OD=R\tan x$

$\therefore$ Height of tower $=$R tan x.