Given:
The distance from the tree to the man = 20m.
The angle of elevation is 25 degrees.
The man's eyes are at a height of 2m.
Required:
We need to find the height of the tree.
Explanation:
Let h be the height of the tree.
[tex]h=2+x[/tex]Since 2m is the distance from the ground to the man's eye.
Consider the triangle ABC.
Here Opposite side =BC=x, Adjacent sides = AB=20m,
Use tan formula.
[tex]tan\theta=\frac{Opposite\text{ side}}{Adjacent\text{ side}}[/tex][tex]\text{ Substitute }\theta=25^o\text{ , Opposite side =x, and Adjacent sides = AB=20m in the formula.}[/tex][tex]tan25^o=\frac{x}{20}[/tex][tex]x=20\times tan25^o[/tex][tex]x=9.3261[/tex]Substitute x =9.3161 in h=2+x .
[tex]h=2+9.3261[/tex][tex]h=11.3261[/tex]Final answer:
The height of the tree is 11.33 m.
