SOLUTION: A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of

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Question 213742: A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of depression of the foot of the building is 26degrees, calculate the height of the building.
Answer by drj(1380) About Me  (Show Source):
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A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of depression of the foot of the building is 26degrees, calculate the height of the building.

Step 1. Let d be the distance to the building from the window. Given depression angle is 26 degrees and the height of the window is 7 meters, then we have the opposite side is 7 and the adjacent side is x. In this case, we have

tan%2826%29=7%2Fd

d=14.3 metres

Step 2. Let x = be the height above seven metre reference, then total height of building h=x+. Then from the window looking at the building we have an angle of elevation of 23 degrees. Then the opposite side is x and the adjacent side is d. We have

tan%2823%29=x%2Fd=x%2F14.3

x=14.3tan%2823%29

x=6.07+metres

Step 3. Then h=6.07+7=13.07 or 13.07 metres

I hope the above steps were helpful.

And good luck in your studies!

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Respectfully,
Dr J