Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°. How high is the tree top from ground?

Answer: Option D

Solution

Answer: Option D

Solution:

Let PQ be three and M and N be positions where Mphan stands.
$$\begin{array}{rl}& \text{Now,}\text{tan}45^{\circ }=1=\frac{PQ}{MQ}\\ & \therefore PQ=MQ\\ & \tan 30^{\circ }=\frac{1}{\sqrt{3}}=\frac{PQ}{NQ}\\ & =\frac{PQ}{10+MQ}\\ & \therefore 10+MQ=\sqrt{3}PQ\end{array}$$
$$\therefore 10+PQ=\sqrt{3}PQ$$     (As, PQ = MQ)
$$\therefore PQ=\frac{10}{\sqrt{3}-1}\text{cm}$$