SOLUTION: Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to b

Algebra ->  Trigonometry-basics -> SOLUTION: Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to b      Log On


   

Question 628645: Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 25°11'. He then drives 1 mile (5280 ft) more and measures the angle of elevation to be 32°51'. Find the height of the mountain to the nearest foot.
Answer by lwsshak3(11628) About Me  (Show Source):
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Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 25°11'. He then drives 1 mile (5280 ft) more and measures the angle of elevation to be 32°51'. Find the height of the mountain to the nearest foot
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Draw a right triangle with the vertical leg representing the height of the mountain=y
Draw a horizontal leg to the point of the 2nd measurement=x
Continue this horizontal leg to the point of the first measurement=x+5280
You now have two right triangles to work with.
Both triangles have a common vertical leg=y
One triangle has a horizontal leg of x with the angle of elevation=32º51'=32.85º
The other triangle has a horizontal leg of x+5280 with the angle of elevation=25º11'=25.18º
..
y=x*tan32.85º=.65x
y=(x+5280)*tan25.18º=.47x+2482.33
..
.65x=.47x+2482.33
.18x=2482.33
x≈13791
y=.65x
y=8964 ft