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 feet.

Step-by-step explanation:

Please find the attachment.

Let h represent the height of the tree.

We have been given that 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°.

We know that tangent relates opposite side of right triangle with its adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(50^{\circ})=\frac{h}{40}$

$1.191753592594=\frac{h}{40}$

$1.191753592594\times 40=\frac{h}{40}\times 40$

$47.67014370376=h$

$h=47.67014370376$

Round to nearest tenth:

$h\approx 47.7$

Therefore, the tree is 47.7 feet tall.