Question

find the length of the third side. if necessary, round to the nearest tenth. 25 16 answer attempt 1 out of 2

Explanation:

Step1: Identify the hypotenuse

The hypotenuse $c = 25$, and one - side $a = 16$. We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $b$ is the unknown side.

Step2: Rearrange the Pythagorean theorem

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

Step3: Substitute the values

Substitute $c = 25$ and $a = 16$ into the formula: $b=\sqrt{25^{2}-16^{2}}=\sqrt{(25 + 16)(25 - 16)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). So $b=\sqrt{41\times9}=\sqrt{369}$.

Step4: Calculate the value

$\sqrt{369}\approx19.2$

Answer:

$19.2$