Question

the manager of a car dealership wants to attach a rope with flags to the top of a pole and to a stake in the ground, as shown in the diagram. based on the diagram, what is the distance in feet from the top of the pole to the bottom of the stake?

Explanation:

Step1: Identify the problem type

This is a right - triangle problem.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 26\) (height of the pole) and \(b=19.5\) (distance from the base of the pole to the stake). We want to find \(c\) (distance from the top of the pole to the stake).
\[c=\sqrt{a^{2}+b^{2}}=\sqrt{26^{2}+19.5^{2}}\]
\[c=\sqrt{676 + 380.25}=\sqrt{1056.25}\]
\[c = 32.5\]

Answer:

32.5