question_answer

At a point on the ground the angle of elevation of a tower is such that its cotangent is 3/5. On walking 32 metres towards the tower the cotangent of the angle of elevation is 2/5. The height of the tower is

A) 160 m

B) 120 m

C) 64 m

D) None of these

Correct Answer: A

Solution :

\[\cot \alpha =\frac{3}{5}\], \[\cot \beta =\frac{2}{5}\], \[32=h\cot \alpha -h\cot \beta \] \[h=\left( \frac{32}{\cot \alpha -\cot \beta } \right)\] \[=\frac{32}{1/5}=160m\].