Question

find the length of the third side. if necessary, write in simplest radical form. $sqrt{58}$ 3 answer attempt 1 out of 2

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $a$ and $b$ are the legs. Let the unknown side be $x$.

Step2: Substitute known values

We know $c = \sqrt{58}$, $b = 3$, so $x^2 + 3^2 = (\sqrt{58})^2$

Step3: Simplify the equation

$x^2 + 9 = 58$

Step4: Solve for $x^2$

$x^2 = 58 - 9 = 49$

Step5: Find $x$

$x = \sqrt{49} = 7$

Answer:

7