Draw a diagram. You have a pyramid with base ABC and summit at S.
I am assuming that S is at the top of a vertical face containing BC.
You have base angles
A = 80
B = 61
so, C=39
side c = 400
So, now you can figure sides a and b using the law of sines.
Hmm. Still can't pin down S. All we know is that is is 23° up from A. Without knowing some other piece of information, there's no way to find the height. Even my initial supposition is not necessarily true.
Demi would like to estimate the height of the hill from its base. Using a compass, she found that the angle between C and B, from A, was 80 degrees. She also estimated the angle from horizontal to the summit to be 23 degrees. She then walked 400 m to B where she measured the angle between A and C to be 61 degrees. Use her information to determine the height of the hill.
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