In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive x = 17 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Round your answer to one decimal place.)
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Let,
distance from
h=x.tan(9), ===> x = h.cot(9) ..................... [1],
Also,
h =(x+17).tan(3.5) = h.cot(9).tan(3.5) + 17.tan(3.5)
h[1-cot(9).tan(3.5)] = 17.tan(3.5) = 1.04,
h = 1.04 / [1 - 0.39] = 1.7 miles >=================< ANSWER