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 12.

Step-by-step solution

Step 1. Given Information 

The given triangle is

Step 2. Apply Pythagoras Theorem

• The length of one of the legs of the given triangle is 16. So, $a=16$.
• The length of the hypotenuse is 20. So, $c=20$.
• Substitute the values in the equation of Pythagoras theorem, $a^2+b^2=c^2$and solve for the unknown side.

$$\begin{gathered} {16}^2+b^2={20}^2 \\ 256+b^2=400 \\ {b}^2=144 \\ b=12 \end{gathered}$$

• So, the length of the unknown leg is 12.

Step 3. Conclusion

The length of the unknown leg is 12.