SOLUTION: While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain

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Question 289726: While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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While traveling across flat land, you notice a mountain directly in front of you.
The angle of elevation to the peak is 2.5 degrees.
After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees.
Approximate the height of the mountain.
:
represent this with a scalene triangle, where
A = 2.5 degrees
B = (180-9) = 171 degrees
C = 180 - 171 - 2.5 = 6.5 degrees
c = 17
Find side b using the law of sines: c%2Fsin%28c%29 = b%2Fsin%28b%29
17%2Fsin%286.5%29 = b%2Fsin%28171%29
:
Sin(6.5)b = 17*sin(171)
:
.1132b = 2.659
b = 2.659%2F.1132
b = 23.49 mi (from angle A to the top of the mountains)
:
Side b is the hypotenuse of a right triangle at the base of the mountain
formed by the mountain top and a line to point A
:
Use the sine of 2.5,
height (h) of the mountain will be the side opposite
Sin(2.5) = h%2F23.49
.0436 = h%2F23.49
h = .0436 * 23.49
h = 1.02462 mi is the mountain height
0r
1.02462 * 5280 = 5410 ft high