Question 218202: can anyone help me with these question pls....thanks..
1. From a point due west from the base of the building, the angle of elevation to the top is 65 degrees. At a point 62 meters further, the angle of elevation is 54 degrees. How tall is the building?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tan(65) = x/y means x = y*tan(65)
tan(54) = x/(y+32) means x = (y+32)*tan(54) = y*tan(54) + 32*tan(54)
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since they both equal to x, then they are equal to each other, so we get:
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y*tan(65) = y*tan(54) + 32*tan(54)
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subtract y*tan(54) from both sides of the equation to get:
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y*tan(65) - y*tan(54) = 32*tan(54)
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factor out the y on the left hand side of the equation to get:
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y*(tan(65)-tan(54)) = 32*tan(54)
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divide both sides of this equation by (tan(65)-tan(54)) to get:
y = 32*tan(54) / (tan(65)-tan(54))
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solve for y to get:
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y = 57.33991401
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Since x = y*tan(65), substitute for y to get:
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x = 57.33991401*tan(65) = 122.9658424
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height of the building is 122.9658424 meters.
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since y = 57.33991401, then
(y+32)*tan(54) = x becomes:
89.33991401*tan(54) = x = 122.9658424 meters once again.
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height is confirmed to be true because both points yield the same height.
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your answer is:
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height of the building is 122.97 meters rounded to the nearest hundredth of a meter.
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a picture of your problem can be found by clicking on the following hyperlink.
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Problem Number 218202 Picture
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