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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.)
