Question

3 the length of the legs of a right triangle are 6 in. and 8 in. use the pythagorean theorem to determine the length of the hypotenuse. show your work.

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

Step2: Substitute values of $a$ and $b$

Let $a = 6$ and $b = 8$. Then we have $6^{2}+8^{2}=c^{2}$. Calculate $6^{2}=36$ and $8^{2}=64$. So, $36 + 64=c^{2}$, which simplifies to $100=c^{2}$.

Step3: Solve for $c$

Take the square root of both sides. Since $c$ represents the length of a side of a triangle, we take the positive square root. $\sqrt{100}=c$, so $c = 10$.

Answer:

$10$ in.