question_answer

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 R is the circum-radius of the triangle ABC, then the height of the tower is [EAMCET 1994]

A) \[R\sin \alpha \]

B) \[R\cos \alpha \]

C) \[R\cot \alpha \]

D) \[R\tan \alpha \]

Correct Answer: D

Solution :

Since the tower makes equal angles at the vertices of the triangle, therefore foot of the tower is at the circumcentre. From \[\Delta OAP,\] we have \[\tan \alpha =\frac{OP}{OA}\] \[\Rightarrow \] \[OP=OA\tan \alpha \] \[\Rightarrow \] \[OP=R\tan \alpha \].