SOLUTION: A backpacker notes that from a certain point on level ground, the angle of elevation to a point at the top of a tree is 34°. After walking 50 feet closer to the tree, the backpacke

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Question 938291: A backpacker notes that from a certain point on level ground, the angle of elevation to a point at the top of a tree is 34°. After walking 50 feet closer to the tree, the backpacker notes that the angle of elevation is 54°. Find the height of the tree.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Who walks around with a protractor?
Let's call his original distance from the tree, X.
Then the second distance is X-50
The tree height is H.
tan%2834%29=H%2FX
tan%2854%29=H%2F%28X-50%29
So then,
%28H%2FX%29%2F%28H%2F%28X-50%29%29=tan%2834%29%2Ftan%2854%29
%28X-50%29%2FX=0.49
X-50=0.49X
0.51X=50
X=98ft
Then,
H%2F98=0.6745
H=66.1ft