Question

an electrician needs to run a cable from the top of a 72 - foot tower to a transmitter box located 21 feet away from the base of the tower. find how long he should make the cable. the length of the cable is \\( \square \\) ft.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 21\), \(b=72\), and \(c\) is the length of the cable.

Step2: Substitute values

Substitute \(a = 21\) and \(b = 72\) into the formula: \(21^{2}+72^{2}=c^{2}\).
Calculate \(21^{2}=441\) and \(72^{2}=5184\). Then \(441 + 5184=c^{2}\), so \(c^{2}=5625\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{5625}\). Since \(\sqrt{5625}=75\).

Answer:

75