Question

A length of cable is attached to the top of a 16-foot pole. The cable is anchored 12 feet from the base of the pole. What is the length of the cable?

A) 16 feet
B) 20 feet
C) 24 feet
D) 28 feet

Answer 1

Using the Pythagorean theorem, the length of the cable is determined to be 20 feet, which corresponds to option B.

Step-by-step explanation:

To find the length of the cable, we will use the Pythagorean theorem since the cable, pole, and the distance from the pole to where the cable is anchored form a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Let's denote:

• The length of the pole as 'a' = 16 feet
• The distance from the pole to where the cable is anchored as 'b' = 12 feet
• The length of the cable as 'c'

According to the Pythagorean theorem:

c² = a² + b²

Plugging in the values we get:

c² = 16² + 12²

c² = 256 + 144

c² = 400

Now, we take the square root of both sides to find 'c':

c = √400c = 20 feet

Therefore, the length of the cable is 20 feet, which corresponds to option B.