Question

The long leg of a right triangle is 49 ft longer than the short leg. The hypotenuse is 61 feet long. How long are the legs of the right triangle?

Answer 1

Using pythagorean theorem:

$c^2=a^2+b^2$

Solve for b:

$\begin{gathered} c^2=(49b)^2+b^2 \\ c^2=2401b^2+b^2 \\ 3721=2402b^2 \\ b^2=\frac{3721}{2402} \\ b=\sqrt[]{\frac{3721}{2402}} \\ b\approx1.2446 \end{gathered}$

Therefore:

$\begin{gathered} a=49(1.2446) \\ a\approx60.9873 \end{gathered}$