Question

Sally was standing 30 feet from a tree. The angle of
elevation from her eyes (4 feet above the ground)
to the top of the tree was 38°. How tall is the tree?
Round your answer to the nearest foot.

Answer 1

Answer:

The tree is 27 feet tall

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle BCD find the value of segment CD

$tan(38^o)=\frac{CD}{BD}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the given value

$tan(38^o)=\frac{CD}{30}$

solve for CD

$CD=tan(38^o)(30)=23\ ft$

step 2

Find the height of the tree

The height of the tree is given by

$CE=CD+DE$

we have

$CD=23\ ft\\DE=4\ ft$

substitute

$CE=23+4=27\ ft$

therefore

The tree is 27 feet tall