Finding the Length of the Missing Side of a Right Triangle

Find the length of the missing side of the right triangle in Figure 5.

Figure 5

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
As we have measurements for side b and the hypotenuse, the missing side is a.

$\begin{matrix} a^{2} + b^{2} & = & c^{2} \\ a^{2} + {(4)}^{2} & = & {(12)}^{2} \\ a^{2} + 16 & = & 144 \\ a^{2} & = & 128 \\ a & = & \sqrt{128} \\ = & 8 \sqrt{2} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the Pythagorean Theorem to solve the right triangle problem: Leg a measures 4 units, leg b measures 3 units. Find the length of the hypotenuse.

How did it go?