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.

valval2205 Feb 20, 2020

#1**+3 **

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 !!!!

CPhill Feb 21, 2020