Question

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

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

Answer 1

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

OP subtends same angle at A, B, C
OP/OA = tan $\alpha$
h = R tan $\alpha$

$\tan \alpha =\frac{h}{R}$
$h=R\tan \alpha$