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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  1. 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.

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