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Andrew [12]
2 years ago
14

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 depressi

on 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?

Mathematics
1 answer:
irina [24]2 years ago
5 0

Answer:

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

so

64-19.19=44.81\ ft

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