Question 1043600: to measure the height of Lincoln's head on mt.rushmore, two sightings 800 feet from the base of the mountain are taken, if the angle of elevation to the bottom of Lincoln's face is 32°, and the angle of elevation to the top is 35 °, what is the height, in feet, of Lincoln's face?
Answer by Boreal(15235)   (Show Source):
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The horizontal line is 800 feet, and the angle to the bottom
is 32 degrees. Tangent 32 = opposite/adjacent, and opposite is the vertical height.
800 tan 32= opposite =499.89 feet
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For the height of the top, it is 800 tan 35, and that is 560.17 feet. The difference between the two is 60.27 feet, if rounding is done only at the end. An alternative way is 80 (tan 35- tan 32), which will round at the end.
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