Quandaries and Queries


Here's my question:
A right triangle (roof of a house)  has a base of 7 feet and a 22 degree angle.  What is the height of the roof and what is the hypotenuse of the triangle.
Thank you.



I drew a diagram and labeled the height of the roof as h feet.

From the diagram the tangent of 22o is h/7, and hence

h = 7 tan(22o) = 7 0.4040 = 2.83 feet,

which is very close to 2 feet 10 inches.

If the hypotenuse of the triangle is of length r feet then Pythagoras' theorem tell us that

r2 = 72 + h2 = 49 + 2.832 = 57.00 feet squares


r = sqrt(57.00) = 7.55 feet,

which is approximately 7 feet 6 and 5/8 inches.



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