Question

In the following exercises, use the Pythagorean theorem to find the length of the leg. Round to the nearest tenth if necessary.

Short answer

The length of the hypotenuse is$8.6$approximately.

Step-by-step solution

Step 1. Given Information

The given triangle is

Step 2. Apply Pythagoras Theorem

• The lengths of the legs of the given triangle are 5 and 7. So, $a=5$and $b=7$.
• Use the Pythagoras theorem ${\mathit{a}}^{\mathbf{2}}\mathbf{+}{\mathit{b}}^{\mathbf{2}}\mathbf{=}{\mathit{c}}^{\mathbf{2}}$and solve to find the hypotenuse of the triangle.

$$\begin{gathered} 5^2+7^2=c^2 \\ 25+49=c^2 \\ {c}^2=74 \\ c\approx 8.6 \end{gathered}$$

• So, the length of the hypotenuse is$8.6$approximately.

Step 3. Conclusion

The length of the hypotenuse is$8.6$approximately.