Question

A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display as shown. How far from the base of the pole should the end of the string of lights be anchored?

Short answer

The distance of the string from the pole is 5 feet.

Step-by-step solution

Step 1. Given Information 

The given image of the pole and string is

Step 2. Use Pythagoras Theorem

• The string forms the hypotenuse of a right angles triangle with the land and the pole as the legs.
• Use, the Pythagoras theorem $a^2+b^2=c^2$and substitute $a=12$and $c=13$in the equation. SOlve to find the value of the unknown variable.

$$\begin{gathered} {12}^2+b^2={13}^2 \\ 144+b^2=169 \\ {b}^2=25 \\ b=5 \end{gathered}$$

• So, the distance of the string from the pole is 5 feet.

Step 3. Conclusion

The distance of the string from the pole is 5 feet.