Question

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Short answer

The length of the missing side is $8.1$.

Step-by-step solution

Step 1. Given Information 

We are given a right-angled triangle whose length of the legs are $7$and $4$.

The objective is to find the length of the hypotenuse.

Step 2. Concept Used  

The Pythagorean Theorem states that in any right triangle, $a^2+b^2=c^2$where c is the length of the hypotenuse anda andb are the lengths of the legs.

Step 3. Find the length of the hypotenuse

As the length of the two legs are $7$and $4$, so in the equation $a^2+b^2=c^2$substitute $7$for $a$and $4$for role="math" $b$.

$\begin{array}{rcl}{7}^2+4^2& =& c^2\\ 49+16& =& c^2\\ 65& =& c^2\end{array}$

Taking square root both sides we get

$\begin{array}{rcl}\sqrt{65}& =& \sqrt{c^2}\\ 8.1& \approx & c\end{array}$

So the length of the hypotenuse is $8.1$.