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 and $a$ and $b$ are the legs. Here, if the hypotenuse is 15 and one leg is 12, then $x^{2}+12^{2}=15^{2}$.

Step2: Rearrange the equation

$x^{2}=15^{2}-12^{2}$.

Step3: Calculate the squares

$15^{2}=225$ and $12^{2}=144$. So $x^{2}=225 - 144$.

Step4: Subtract

$x^{2}=81$.

Step5: Solve for $x$

$x=\sqrt{81}=9$.

Answer:

9