Question

problem 10: spiral review determine the exact length of the unlabeled side.

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem for a right - triangle $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs.

Step2: Substitute values

Let $a = 4$ and $b = 7$. Then $c^{2}=4^{2}+7^{2}$.

Step3: Calculate squares

$4^{2}=16$ and $7^{2}=49$, so $c^{2}=16 + 49=65$.

Step4: Solve for $c$

$c=\sqrt{65}$.

Answer:

$\sqrt{65}$