Question

The horizontal distance between two trees of different heights is$60m.$ The angle of depression of the top of the first tree, when seen from the top of the second tree, is$45$ degree. If the height of the second tree is $80m$, find the length of the first tree.

• A. $20m$
• B. $24m$
• C. $40m$
• D. $64m$

Answer 1

The correct option is A

$20m$

Let $AS$be the second tree and$BF$ be the first tree.

$$\begin{gathered} BF=CS=x \\ \tan {45}^o=\frac{AC}{BC} \\ 1=\frac{(80-x)}{60} \\ 80-x=60 \\ x=20 \end{gathered}$$

Thus, height of the first tree$=20m.$

Hence, option A is the correct option.