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.
Hi,
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
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
thus
r = sqrt(57.00) = 7.55 feet,
which is approximately 7 feet 6 and 5/8 inches.
Penny