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# Surveyors are trying to determine the height of a mountain by taking measurements from a level plane.

6. Surveyors are trying to determine the height of a mountain by taking measurements from a level plane. They are able to measure angles of elevation using a sextant and they are able to measure horizontal distances using a laser range-finder together with a reflector.From a particular location A, they find the angle of elevation from the horizontal to the top of the mountain to be19.2?. After walking 900 feet closer to the mountain to location B, they find the angle of elevation to the top of the mountain to now be 22.7?.a. Draw a careful diagram that includes all of the given information. Introduce variables to represent the unknowns, including both the distance, x, from point B to the “center” of the mountain (a point at the same elevation as A and B but directly below the peak) and the height, h, of the mountain. You may neatly draw the diagram by hand and insert a quality picture of it into your write up.b. Use the given i nformation and appropriate i deas i nvolving trigonometric f unctions to find two different equations that i nvolve the unknown variables x and h. Wor k with exact values r ather than approximations.(For example, if at s ome point you had the quantity ” sin(33?),” keep using the quantity in that form, rather than a decimal approximation of the quantity.)