Question

question
find the length of the third side. if necessary, write in simplest radical form.
triangle image with hypotenuse 7, one leg \\(\sqrt{13}\\), right - angled

Explanation:

Step1: Identify known sides, hypotenuse

We have a right triangle: one leg $a=\sqrt{13}$, hypotenuse $c=7$, unknown leg $b$.

Step2: Apply Pythagorean theorem

The theorem is $a^2 + b^2 = c^2$. Rearrange to solve for $b$:
$b^2 = c^2 - a^2$

Step3: Substitute values into formula

$b^2 = 7^2 - (\sqrt{13})^2 = 49 - 13 = 36$

Step4: Solve for $b$

Take square root of both sides:
$b = \sqrt{36} = 6$

Answer:

6