Question

You are standing 40 meters from the base of a palm tree that is leaning 8° from the vertical away from you. The angle of elevation from your feet to the top of the tree is 20.5°.

Answer 1

Explanation

To get the answer, we will have to sketch the diagram below

Thus, the angle at B is

$90^0+8^0=98^0$

The angle at A is

$20.5^0$

The length of the tree is Y

so the angle at C will be

$180^0-98^0-20.5^0=61.5^0$

Part B

The value of Y can be calculated using the sine rule

$\frac{\sin61.5^0}{40}=\frac{\sin 20.5^0}{y}$

The value of y will be

$\begin{gathered} y=\frac{40\times\sin 20.5^0}{\sin 61.5^0} \\ \\ y=\frac{14.01}{0.8788} \\ \\ y=15.942 \\ \\ y=15.9m \end{gathered}$

The value of y = 15.9 m