From the top of 75 m high tower, the angle of depression of two points P and Q on opposite side of the base of the tower on level ground is and , such that = 3/4 and = 5/8. What is the distance between the points P and Q?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Let }AB\text{ be the tower}\text{.}\\ & \text{Given that;}\\ & \tan \theta =\frac{3}{4},\tan \varphi =\frac{5}{8}\\ & \text{In }\Delta ABP,\\ & \tan \theta =\frac{AB}{PB}\\ & \frac{3}{4}=\frac{75}{PB}\\ & PB=100\text{ m}\\ & \text{In }\Delta ABQ,\\ & \tan \varphi =\frac{AB}{BQ}\\ & \frac{5}{8}=\frac{75}{BQ}\\ & BQ=120\text{ m}\\ & \text{Hence, the distance between }P\text{ and }Q\\ & =100+120\\ & =220\end{array}$$