SOLUTION: base of tool shed is 18 by 18 feet. the height of the rectangular side is 9 feet. the builder is considering using an angle that measures 125 degrees. determine the surface area of

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Question 953663: base of tool shed is 18 by 18 feet. the height of the rectangular side is 9 feet. the builder is considering using an angle that measures 125 degrees. determine the surface area of the roof if the 125 degree angle is used.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The top line of the roof separates the roof space into a cross section with a base 9 feet, an angle of 125%2F2=62%261%2F2 degrees opposite the 9 foot base, and this is a right triangle. The other angle along the top edge of the shed, the square part, is 180-90-62%261%2F2=27.5 degrees.

You want to know the hypotenuse which is one of the dimensions of half of the roof.

cos%2827.5%29=h%2F9, h for hypotenuse;
h=9%2Acos%2827.5%29

Now, ONE surface of the roof is 9%2A9cos%2827.5%29; and there are two of these, so the entire roof surface area is highlight%282%2A9%2A9cos%2827.5%29%29


(I know, a picture would help.)