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 unknown leg is$\sqrt{105}$.

Step-by-step solution

Step 1. Given Information 

The given triangle is

Step 2. Apply Pythagoras Theorem

• In the given triangle, the length of one of the legs is 8. So, $a=8$.
• The length of the hypotenuse is 13. So, $c=13$.
• Substitute the values into the Pythagoras Theorem, and solve for the unknown variable b.

$$\begin{gathered} 8^2+b^2={13}^2 \\ 64+b^2=169 \\ {b}^2=105 \\ b=\sqrt{105} \end{gathered}$$

• So, the length of the unknown side is $\sqrt{105}$.

Step 3. Conclusion

The length of the unknown side is $\sqrt{105}$.