Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \text{Now,}\text{tan}45^{\circ }=1=\frac{PQ}{NQ}\\ & \therefore \text{Tree}\text{height}\\ & =PQ=NQ\\ & =\left(240+MQ\right)\\ & \tan 60^{\circ }=\sqrt{3}\\ & =\frac{PQ}{MQ}\\ & =\frac{240+MQ}{MQ}\\ & \therefore 240+MQ=\sqrt{3}MQ\\ & \therefore MQ=\frac{240}{\sqrt{3}-1}\text{ft}\\ & \therefore NQ=240+MQ\\ & =\frac{240\sqrt{3}}{\sqrt{3}-1}\text{ft}\end{array}$$
= Rohit was this much far away initially