SOLUTION: A cable to the top of a tower makes an angle of 31deg with the level ground. At a point 100 yards closer to the tower the angle of elevation to the top of the tower is 57deg. Estim

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Question 70821: A cable to the top of a tower makes an angle of 31deg with the level ground. At a point 100 yards closer to the tower the angle of elevation to the top of the tower is 57deg. Estimate the length of the cable.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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cable to the top of a tower makes an angle of 31deg with the level ground. At a point 100 yards closer to the tower the angle of elevation to the top of the tower is 57deg. Estimate the length of the cable.
:
If the angle to the tower is 57 we know the interior angle is 180 - 57 = 123
Let that angle be A and find the side opposite which is a
:
The third angle, which is opposite 100 yds is: 180 - 123 - 31 = 26 degrees
:
Use the law of sines:
Sin%28123%29%2Fa = Sin%2826%29%2F100
:
.83867%2Fa = .43837%2F100
:
Cross multiply:
.43837a = .83867*100
:
a = 83.867%2F.43837
:
a = 191.3 yds