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

Answer:

$47.7\ ft$

Step-by-step 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

$tan(50\°)=\frac{BC}{AC}$

The tall of the tree is BC

$BC=ACtan(50\°)$

$AC=40\ ft$

substitute

$BC=40*tan(50\°)=47.7\ ft$

Answer 2

Tan(angle) = opposite length/ adjacent length

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