SOLUTION: A tree in an open field stands on top of a uniformly shaped mound. When the angle of elevation of the sun is 38 degrees, the shadow of the tree ends at the base of the mound which

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Question 842397: A tree in an open field stands on top of a uniformly shaped mound. When the angle of elevation of the sun is 38 degrees, the shadow of the tree ends at the base of the mound which is 42 ft. down from the base of the tree. If the mound rises at an angle of 7 degrees, how tall is the tree?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Segment CD represents the tree. The green triangle represents the mound.
h= height of the tree.
AC =42ft
ABC and ABD are right triangles.
x=%2842ft%29%2Acos%287%5Eo%29+=approximately41.687ft
y=%2842ft%29%2Asin%287%5Eo%29+=approximately5.1185ft
y%2Bh=x%2Atan%2838%5Eo%29+=approximately0.781286
h=x%2Atan%2838%5Eo%29-y
Substituting the approximate values above,
h=%2841.687ft%29%2A0.781286-5.1185ft=approximatelyhighlight%2827.451ft%29
Working further with formulas instead,
h=%2842ft%29%2Acos%287%5Eo%29%2Atan%2838%5Eo%29-%2842ft%29%2Asin%287%5Eo%29+=approximatelyhighlight%2827.451ft%29