Question

1. if a 35 - foot cable was run from the top of the pole and anchored to the ground at a distance from the pole, about how far away from the pole would it be anchored?
2. if the telephone pole was 2 feet taller, and the cable was still anchored to the ground 15 feet away from the pole how would the change in pole height affect the length of the cable

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 30\) (height of the pole), \(c = 35\) (length of the cable), and \(b\) is the distance from the pole.
Substitute the values: \(30^{2}+b^{2}=35^{2}\).

Step2: Calculate the squares

\(30^{2}=900\) and \(35^{2}=1225\). So the equation becomes \(900 + b^{2}=1225\).

Step3: Solve for \(b^{2}\)

Subtract 900 from both sides: \(b^{2}=1225 - 900=325\).

Step4: Find \(b\)

\(b=\sqrt{325}\approx18\) (rounded to the nearest whole number).

Answer:

The cable would be anchored about 18 feet away from the pole.