Answer:
The distance between the tree and the tower is 18.48 meters.
Step-by-step explanation:
We are given the following information in the question:
Height of tower = 30 m
Height of man = 2 m
Angle of depression = 30 degrees
We have to find the distance between the tree and the tower.
The attached image shows the scenario.
Formula:
[tex]\text{Tan(Angle of Depression)} = \displaystyle\frac{\text{Perpendicular}}{\text{Base}} = \frac{\text{Distance between tower and tree}}{\text{Height of tower + Height of man}}\\\\= \tan(30) = \frac{\text{Distance between tower and tree}}{32}\\\\\frac{1}{\sqrt3} = \frac{\text{Distance between tower and tree}}{32}\\\\\text{Distance between tower and tree} = \frac{32}{\sqrt3} = 18.48~m[/tex]
Thus, the distance between the tree and the tower is 18.48 meters.
