SOLUTION: cindy is standing at a point A west of a mountain. From point A, the angle of elevation to the top of the mountain is 32 degrees. From point B, which is 8325 feet to the east of po

Question 1169665: cindy is standing at a point A west of a mountain. From point A, the angle of elevation to the top of the mountain is 32 degrees. From point B, which is 8325 feet to the east of point A (and east of the mountain) the angle of elevation to the top of the mountain is 42 degrees. Determine the height of the mountain to the nearest tenth of a foot.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this
x distance from point A to the base of the mountain directly under the summit.
8325-x from the base to point B
tan 42= h/(8325-x)
tan 32=h/x
(8325-x)*tan 42=h=x tan 32
tan 32/tan 42=(8325-x)/x
0.6940x=(8325-x)
1.6940x=8325 ft
x=4914.40 feet to the base,
tan 32=h/4914.40=0.6249
so h=3070.9 feet.
check for the other side
B is therefore 3410.6 feet from the base.
If the height is 3070.9 feet, then tangent is 3070.9/3410.6 and that is 42 degrees.
The mountaintop is 3070.9 feet above the observer.

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