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 $20$.

Step-by-step solution

Step 1. Given Information 

We are given a right-angled triangle whose length of the hypotenuse is $25$and length of one leg is $15$.

The objective is to find the length of the missing side.

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 missing length 

As the length of the hypotenuse is $25$and the length of one leg is $15$, so in the equation $a^2+b^2=c^2$substitute $25$for $c$and $15$for $a$.

$\begin{array}{rcl}{15}^2+b^2& =& {25}^2\\ 225+b^2& =& 625\\ b^2& =& 625-225\\ b^2& =& 400\end{array}$

Taking square root both sides we get

$\begin{array}{rcl}\sqrt{b^2}& =& \sqrt{400}\\ b& =& 20\end{array}$

So the length of the missing side is $20$.