SOLUTION: To estimate the height of a building above a level plain, a surveyor measures the angle of elevation to the top of the building to be 28.5 degrees. Three hundred feet closer to the

Algebra ->  Trigonometry-basics -> SOLUTION: To estimate the height of a building above a level plain, a surveyor measures the angle of elevation to the top of the building to be 28.5 degrees. Three hundred feet closer to the      Log On


   

Question 1040554: To estimate the height of a building above a level plain, a surveyor measures the angle of elevation to the top of the building to be 28.5 degrees. Three hundred feet closer to the building the angle of elevation is 32.5 degrees. Estimate the height of the building. Round your answer to the nearest foot.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = the height of the building
Let +d+ = distance in the 1st case from
surveyor to base of building
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(1) +tan%28+28.5+%29+=+h%2Fd+
(2) +tan%28+32.5+%29+=+h%2F%28+d+-+100+%29+
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(1) +.54296+=+h%2Fd+
(2) +.63707+=+h%2F%28+d+-+100+%29+
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(1) +h+=+.54296d+
(2) +h+=+.63707%2A%28+d+-+100+%29+
Substitute (1) into (2)
(2) +.54296d+=+.63707d+-+63.707+
(2) +.09411d+=+63.707+
(2) +d+=+676.94+
and
(1) +h+=+.54296d+
(1) +h+=+.54296%2A676.94+
(1) +h+=+367.55+
The height is 368 ft to the nearest foot
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check answer:
(1) +.54296+=+h%2Fd+
(1) +.54296+=+367.55+%2F+676.94+
(1) +.54296+=+.54296+
and
(2) +.63707+=+h%2F%28+d+-+100+%29+
(2) +.63707+=+367.55%2F%28+676.94+-+100+%29+
(2) +.63707+=+367.55+%2F+576.94+
(2) +.63707+=+.63707+
OK