Question

Melissa is standing 40 ft from a tree. The angle of elevation from where she is standing on the ground to the top of the tree is 50°.

How tall is the tree?



Round the final answer to the nearest tenth.

Enter your answer in the box.

Answer 1

Tan(angle) = opposite length/ adjacent length

Tan(50) = h/40
h = 40 x tan(50)
h = 47.67 or 47.7 feet

Answer 2

`47.7\ ft`

Explanation:

see the attached figure to better understand the problem

we know that

In a right triangle the tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

so

In this problem

`tan(50\°)=(BC)/(AC)`

The tall of the tree is BC

`BC=ACtan(50\°)`

`AC=40\ ft`

substitute

`BC=40*tan(50\°)=47.7\ ft`