SOLUTION: Find the height of a flagpole that sits atop a hill, if it makes an angle of 122 degrees with the hillside, and the angle of elevation between the side of the hill to the top of th

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Question 375078: Find the height of a flagpole that sits atop a hill, if it makes an angle of 122 degrees with the hillside, and the angle of elevation between the side of the hill to the top of the flagpole is 35 degrees at a distance of 120 feet.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the height of a flagpole that sits atop a hill, if it makes an angle
of 122 degrees with the hillside, and the angle of elevation between the
side of the hill to the top of the flagpole is 35 degrees at a distance of 120 feet.
:
We are going to use the law of Sines,
:
Let the angle at the top of the pole to a point on the hillside = A
Then the side opposite this angle = a, which is given as 120'
:
Let the angle between the hillside point to the top of the pole = B (35 degrees)
Then the side opposite this angle = b (the height of the pole
:
The angle between the pole and the hillside, C = 122 degrees
:
Find angle A: 180 - 122 - 35 = 23 degrees
:
b%2Fsin%28B%29 = a%2Fsin%28A%29
Using our values
b%2Fsin%2835%29 = 120%2Fsin%2823%29
Cross multiply
sin(23)*b = sin(35)*120
Which is
.39073b = .573576*120
.39073b = 68.829
b = 68.829%2F.39073
b = 176.155 ft is the height of pole above the top of the hill