An electrician needs to run a cable from the top of a 36​-foot tower to a transmitter box located 15 feet away from the base of the tower. Find how long he should cut the cable.

Answer 1

This is a typical Pythagorean Theorem question. A² plus B² equals C². Now, If I were the electrician, I would run the line down the 36 ft. and then horizontally for the extra 15 feet, giving you a total of 51 ft. However, as the crow flies (or falls diagonally) you would need to determine what C² equals. 36² is 1,296. 15² is 225. Together they equal 1,521, which would equal C. Now, we must find the square root of C to square it. The square root of 1,521 is 39. The electrician would need a 39 foot cable.

Answer 2

If you sketch out the drawing of what is described, you will see it makes a right triangle. We are given 2 legs of the triangle and are asked to find the hypotenuse, the length of the cable. To do this, we can use the Pythagorean Theorem.

a²+b²=c² Plugging in the legs

(36)²+(15)²=c² Simplify the square terms

1296+225=c² Add

1521 = c² Take the square root of both sides

√1521 = c

c=39 ft.

The length of the wire should be cut to 39 ft.