a squared + b squared equals 25.84027777777777

Question

Hello. I am working with a house building/design and need to know what the measurements of the legs of a right triangle would be if the length of the hypotenuse is 5'1" (or, 5.083333333333333 ft.). The program I am using does not yet have the ability to measure the angle a wall is placed at. The hypotenuse, placed at that particular needed angle, is 5'1" (or, 5.083333333333333 ft.). What is the length of each of the two legs of the right triangle if the length of the hypotenuse is the number above?

Answer 1

There are many answers to this question, but I guess the one you want must contain whole numbers of inches, so let’s work in inches instead of feet and inches.

61²=a²+b² can be written: b²=61²-a²=(61-a)(61+a).

If a=60, b²=(61-60)(61+60)=121, which is a perfect square.

So b=11 in and a=60 in (5ft).

As it happens, no other whole numbers satisfy the equation.