SOLUTION: Two wires tethered a balloon to the ground (a) 85 degrees and (b) 75 degrees. How high is the balloon above the ground if the length of (a) to (b) is 100 meters?

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Question 1114275: Two wires tethered a balloon to the ground (a) 85 degrees and (b) 75 degrees. How high is the balloon above the ground if the length of (a) to (b) is 100 meters?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Draw picture.
Two right triangles which share the same height (leg).

x, bottom left leg from a
100-x, bottom right leg from b
y, the height of balloon


system%28y%2Fx=tan%2885%29%2Cy%2F%28100-x%29=tan%2875%29%29

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x=y%2Ftan%2885%29
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y%2F%28100-x%29=tan%2875%29
y=%28100-x%29tan%2875%29
y=%28100-y%2Ftan%2885%29%29%2Atan%2875%29
y=100%2Atan%2875%29-y%28tan%2875%29%2Ftan%2885%29%29
y%2By%2A%28tan%2875%29%2Ftan%2885%29%29=100%2Atan%2875%29
y%281%2Btan%2875%29%2Ftan%2885%29%29=100%2Atan%2875%29

highlight%28y=%28100%2Atan%2875%29%29%2F%281%2Btan%2875%29%2Ftan%2885%29%29%29
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