Question

Find the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. Use a calculator to estimate the square root to one decimal place.The length of the leg is approximately _____inches.

Answer 1

The length of the leg a of the right triangle is obtained by applying the Pythagorean theorem which is given as:

$\text{opposite}^2+adjacent^2=hypothenus^2$

Thus, we have that:

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

Given that b = 21.5 inches and c = 31.9 inches, we now have:

$a^2+(21.5)^2=(31.9^2)$$a^2+462.25=1017.61$$a^2=1017.61-462.25$$a^2=555.36$$\begin{gathered} a=\sqrt[]{555.36}=23.57 \\ \Rightarrow a=23.6\text{ inches (to one decimal place)} \end{gathered}$

Therefore, the length of the leg a of the right triangle is 23.6 inches