Question

find the length of the third side. if necessary, round to the nearest tenth. 24 25

Explanation:

Step1: Identify the hypotenuse

The hypotenuse is the longest side of a right - triangle. Here, the hypotenuse $c = 25$ and one side $a = 24$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $b$ is the unknown side. We can rewrite it as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $c = 25$ and $a = 24$ into the formula: $b=\sqrt{25^{2}-24^{2}}$.
First, calculate $25^{2}=625$ and $24^{2}=576$. Then $25^{2}-24^{2}=625 - 576=49$.
So $b=\sqrt{49}=7$.

Answer:

7