Harry is building a house with a sloping roof. If the roof is 44 feet long and 10 feet high, what is the angle that the roof makes with the horizontal?

Question

anonymous · Answer

I tried to draw this situation, but it didn't work, so I'll have to describe what I had drawn.

If you draw this roof, the 44 foot measure is along the slope of the roof, which is the hypotenuse of a right triangle.  The height of the triangle is the 10 foot measure, so it is opposite of the angle we want to find.  If we're trying to relate the angle to the sides opposite and hypotenuse we have to use the sine function.

For this situation, call the angle we want to find x, so: sin(x) = 10/44 which is about .227
To find x, use the sin inverse function with .227, yielding about 13.137 degrees.