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**Problem was initially posted in a technical math section, so is missing the homework template.**

*From a position 150 ft above the ground, an observer in a building measures angles of depression of 12° and 34° to the top and bottom, respectively, of a smaller building, as in the picture on the right. Use this to find the height h of the smaller building.*

I have found that the angle between the observer and the ground is 56°; however, when I use the tangent function to get the distance between the smaller building and the observer [150 tan(56)] I get the wrong answer and I do not understand why. The only solutions to this problem that I have found involve the law of sines, which has not been covered yet. If I knew the distance between the observer and the smaller building (let's call it x), then I would be able to construct a right triangle from the observing to above the smaller building, where the triangle would have acute angles 78 and 12 and a leg of length x; however, I would not know how to proceed from there.

My questions are: why can I not use [150 tan(56)] to calculate x, how do I calculate x, and how do I find h from the triangle with leg x and angles 78 and 12.

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