Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $c^2 = a^2 + b^2$, solve for missing side $b$.

Step2: Rearrange formula for $b$

$b = \sqrt{c^2 - a^2}$

Step3: Substitute given values

$c=25$, $a=7$, so $b = \sqrt{25^2 - 7^2}$

Step4: Calculate squares

$25^2=625$, $7^2=49$, so $b = \sqrt{625 - 49}$

Step5: Compute difference and root

$625-49=576$, $\sqrt{576}=24$

Answer:

24