Question

question 2 5 pts

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, $c = 21$, one leg is $15$, and the other leg is $x$. So, $x^{2}+15^{2}=21^{2}$.

Step2: Rearrange the equation to solve for $x^{2}$

$x^{2}=21^{2}-15^{2}$.

Step3: Calculate the squares

$21^{2}=441$ and $15^{2}=225$. Then $x^{2}=441 - 225=216$.

Step4: Solve for $x$

$x=\sqrt{216}=6\sqrt{6}\approx 14.7$.

Answer:

$6\sqrt{6}$