Question

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

Short answer

The length of the hypotenuse is$10$.

Step-by-step solution

Step 1. Given Information 

We are given a right angled triangle whose lengths of two legs are $8$and $6$.

We need to find the length of the hypotenuse of the triangle.

Step 2. Concept used 

The Pythagorean Theorem states that in any right triangle, $a^2+b^2=c^2$where cis the length of the hypotenuse and aand bare the lengths of the legs.

Step 3. Find the hypotenuse

As the two legs are of length $8$and $6$. So in the equation $a^2+b^2=c^2$substitute $8$for $a$and $6$for $b$.

role="math" localid="1647231920457" $\begin{array}{rcl}{8}^2+6^2& =& c^2\\ 64+36& =& c^2\\ 100& =& c^2\end{array}$

Taking square root both sides we get

$\begin{array}{rcl}\sqrt{100}& =& \sqrt{c^2}\\ 10& =& c\end{array}$

So the length of the hypotenuse is $10$.