Question

find the missing side length of the given right triangle. if necessary, express your answer as a simplified square root. 85 units, \\(\sqrt{85}\\) units, \\(5\sqrt{17}\\) units, \\(\sqrt{13}\\) units

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

Step2: Substitute the values

Here, $a = 6$ and $b = 7$. So we calculate $6^2 + 7^2$.
$6^2 = 36$ and $7^2 = 49$. Then $36 + 49 = 85$.

Step3: Solve for $c$

Taking the square root of 85 (since $c = \sqrt{a^2 + b^2}$), we get $c = \sqrt{85}$.

Answer:

$\sqrt{85}$ units