Question 200796: Trigonometry
4. A building stands 12 metres away from the balcony of Devon's apartment. From his balcony, the angle of elevation to the top of the building is 65 degrees, and the angle of depression to the bottom of the building is 40 degrees. How tall is the building?
Thanks!!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A building stands 12 metres away from the balcony of Devon's apartment. From his balcony, the angle of elevation to the top of the building is 65 degrees, and the angle of depression to the bottom of the building is 40 degrees. How tall is the building?
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Draw the picture.
You have two right triangles.
The upper one has a 65 degree angle opposite part of the height
of the building.
tan(65) = height(above)/12
height above = 12*tan(65) = 25.73 meters
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The lower triangle has a 40 degree angle opposite part of the height
of the building
tan(40) = height(below)/12
height below = 12*tan(40)
height below = 10.069 meters
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Total height = 25.73 + 10.069 = 35.799 meters
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Cheers,
Stan H.
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