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# Trigonometry question

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Corey spies a bald eagle in a tall tree. He estimates the height of the tree to be 80 feet and the angle of elevation to the bird from where he stands to be 65°. The leaves on the tree make it difficult for Corey to watch the bird, so he takes several steps away from the tree to get a better view. He now estimates his angle of elevation to be 41°.

How many feet did Corey step back to gain a better view of the bird? Round your answer to the nearest hundredth of a foot.

Feb 9, 2022

#1
+117861
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Finding this to the nearest hundredth of a foot is rediculus becasue all the given measurmennts are estimations.

It could not be accurate even to the nearest foot, but anyway....

Use trig to find x

then use trig to find   x+y

Then subtract to find y

Feb 9, 2022
#2
+13892
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How many feet did Corey step back to gain a better view of the bird?

Hello Guest!

$$tan\ 41^o=\frac{80\ ft}{\frac{80\ ft}{tan\ 65^o}+y}\\ \frac{80\ ft}{tan\ 65^o}+y= \frac{80\ ft}{tan\ 41^o}\\ y= \frac{80\ ft}{tan\ 41^o}-\frac{80\ ft}{tan\ 65^o}\\ \color{blue}y=54.72\ ft$$

!

Feb 9, 2022
edited by asinus  Feb 9, 2022
#3
+13892
+1

Sorry, I was on my way.

!

asinus  Feb 9, 2022