. The vertical change in elevation from the point where the surveyor is standing to the point on the mountain is __________ miles. (Round your answer to the nearest hundredth of a mile.)
Philip P. answered • 01/10/23
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Draw a picture. You'll get a right triangle. The horizontal leg is the distance from the surveyor to the mountain, 5 miles. The vertical leg is the unknown height of the mountain, call it h. The hypotenuse is from the surveyor to the top of the mountain. The angle formed by the horizontal base and the hypotenuse is 12 degrees.
Now you can use some trig:
tan(12°) = opposite leg/adjacent leg
tan(12°) = h/5
5·tan(12°) = h
Use you calculator to find tan(12°) to get the answer. The units for h are miles.
