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.
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 !!!!