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$8$.

Step-by-step solution

Step 1. Given Information

We are given a right angled triangle whose length of hypotenuse is $17$and length of one leg is role="math" $15$.

The obejctive 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 $17$and the length of one leg is $15$, so in the equation $a^2+b^2=c^2$substitute $17$for $c$and role="math" localid="1647232330742" $15$for $a$.

$\begin{array}{rcl}{15}^2+b^2& =& {17}^2\\ 225+b^2& =& 289\\ b^2& =& 289-225\\ b^2& =& 64\end{array}$

Taking square root both sides we get

$\begin{array}{rcl}\sqrt{b^2}& =& \sqrt{64}\\ b& =& 8\end{array}$

So the length of the missing side is $8$.