<PRE><B>Question 136941</B>
While traveling across flat land, you notice a mountian directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the montain, the angle of elevation is 9 degrees. Approximate the height of the mountain. 
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Because you are looking from two different positions, you have two right
triangles that are similar.
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#1 has a 2.5 degree angle opposite the height of the mountain (h).
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#2 has a 9 degree angle opposite the height of the mountain (h).
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#1 has a base of (17+x) miles (distance to the mountain on the ground)
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#2 has a base of x miles (distance to the mountain on the ground)
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EQUATIONS:
From #1: h = (17+x)*tan(2.5)
From #2: h = x*tan(9)
x*tan(9) = 17*tan(2.5) + x(tan(2.5)
x[tan9 - tan2.5] = 17tan2.5
x = 0.7422/[0.1147
x = 6.469782... miles
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So, h = xtan9 = 1.0247 miles high
h = 1.0247*5280 = 5410.48 ft. high
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Cheers,
Stan H.



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