Question

a man is standing 20m from a large tree. he can see the top of the tree with an angle of elevation of 25 degrees. if the man's eyes are at a height of 2m, what is the height of the tree

Answer 1

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.

Step-by-step explanation:

Let h be the height of the tree.

`h=2+x`

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.

`tan\theta=\frac{Opposite\text{ side}}{Adjacent\text{ side}}`
`\text{ Substitute }\theta=25^o\text{ , Opposite side =x, and Adjacent sides = AB=20m in the formula.}`
`tan25^o=(x)/(20)`

`x=20* tan25^o`
`x=9.3261`

Substitute x =9.3161 in h=2+x .

`h=2+9.3261`

`h=11.3261`

Final answer:

The height of the tree is 11.33 m.