Question 623384: please help me solve this problem: HEIGHT OF A PROBLEM: In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of a mountain.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of a mountain.
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Make a triangle ABC, C is the mountain top, A the 1st point, B the 2nd point.
Angle CAB = 3.5
Angle CBA = 180 - 9 = 171 degs
Angle BCA = 180 - (3.5 + 9) = 5.5 degs
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Find the distance BC = side a
Law of Sines:
c/sin(C) = a/sin(A)
a = c*sin(A)/sin(C) = 9*sin(3.5)/sin(5.5)
a =~ 5.7325 miles
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h = a*sin(180 - 171)
h =~ 0.89676 mi
h =~ 4735 feet
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