Question 215034: 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 degrees and 24'. He then drives 1 mile (1 mile=5280 ft) more and measures the angle of elevation to be 34 degrees and 40'. Find the height of the mountain to the nearest foot.
I'm not allowed to use law of sines, i have to solve it algebraically according to my teacher.
i can set it up and make a drawing and everything, i just can't figure it out.
thank you!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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 degrees and 24'. He then drives 1 mile (1 mile=5280 ft) more and measures the angle of elevation to be 34 degrees and 40'. Find the height of the mountain to the nearest foot.
I'm not allowed to use law of sines, i have to solve it algebraically according to my teacher
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If you have a picture the height of the mountain is "h".
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You two overlapping right triangles involving "h" and the two
different angles.
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tan(25 24/60) = h/x
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tan(34 40/60) = h/(x-5280)
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Therefore 0.4748x = 0.69157(x-5280)
0.4748x = 0.69157x-0.09157*5280)
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-0.2168x = -0.09157*5280
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x = 2230 ft
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Cheers,
Stan H.
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