Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 15$, $a = 9$, and $b=x$. So, $x^{2}+9^{2}=15^{2}$.

Step2: Rearrange the equation

$x^{2}=15^{2}-9^{2}$.

Step3: Calculate the squares

$15^{2}=225$ and $9^{2}=81$. Then $x^{2}=225 - 81=144$.

Step4: Solve for $x$

$x=\sqrt{144}=12$.

Answer:

$12$