Mathematics: You are standing on a small fire tower 50 feet from a tree. You notice a squirrel in the tree. You measure the angle of depression to the base of the tree to be 52∘. The squirrel is at an angle of elevation of 21∘. How many feet off the ground is the squirrel?

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You are standing on a small fire tower 50 feet

tintlemax6256

19.01.2022

44.81 feet

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ACD

Find the length side AC (height of the small fire tower)

$tan(52^o)=\frac{AC}{50}$ ---> by TOA (opposite side divided by the adjacent side)

Solve for AC

$AC=tan(52^o){50}$

$AC=64\ ft$

step 2

In the right triangle ABE

Find the length side AB

$tan(21^o)=\frac{AB}{50}$ ---> by TOA (opposite side divided by the adjacent side)

solve for AB

$AB=tan(21^o){50}$

$AB=19.19\ ft$

step 3

How many feet off the ground is the squirrel?

Subtract the length side segment AB from the length side segment AC

$64-19.19=44.81\ ft$

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