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Measure Height of Mountain : Angle of Elevation

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To measure the height of a mountain a surveyor takes two sightings of the peak at a distance of 900 meters apart on a direct line to the mountain (see attached picture). The first observation results in an angle of elevation of 47 degrees, whereas the second results an angle of elevation of 35 degrees. If the transit is 2 meters high, what is the height h of the mountain?

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Trigonometry is used find the height of a mountain. The solution is detailed and well presented.

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