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1.     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 68°. 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 20, 2020
 #1
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We  can solve this    as follows....

 

We  can find  his initial   distance from  the  tree, D,   thusly

 

tan (68°)  =  80  / D      rearrange as

 

D =  80   / tan (68°)  ≈  32.3  ft

 

Now....let  x  be  the  additional distance that he steps back and we  have that

 

tan  ( 41°)  = 80  /  ( 32.3  + x)     rearrange as

 

(32.3 + x)  tan (41°)   = 80

 

32.3*tan(41°)  +  x *  tan (41°)  =  80

 

x * tan (41°)  =  80  -  32.3 * tan (41°)

 

x =    [  80  - 32.3 * tan (41°)  ]   / tan (41°)  ≈    59.73  ft 

 

The second part  of this problem might be better solved with the  cotangent  because

 

cot (41°)  =  (32.3  + x)   / 80      is a little easier to  solve  !!!!

 

cool cool cool

 Feb 21, 2020
edited by CPhill  Feb 21, 2020

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