An electric pole has a support cable that is attached to the pole 20 ft. from the

Question

ground. The cable is anchored on the ground 10 ft. from the base of the pole. How
long is the cable? Round to the nearest tenth. (1 point)
17.3 ft.
500 ft.
300 ft.
22.4 ft.

Answer 1

To find the length of the cable, we can use the Pythagorean theorem. The situation can be visualized as a right triangle where:

• One leg is the height of the pole at which the cable is attached (20 ft).
• The other leg is the horizontal distance from the base of the pole to the point where the cable is anchored (10 ft).
• The cable, which is the hypotenuse of the triangle, is what we want to find.

Using the Pythagorean theorem:

\[ c^2 = a^2 + b^2 \]

where:

• \( c \) is the length of the cable,
• \( a \) is the height of the cable attachment (20 ft),
• \( b \) is the distance from the base of the pole to the anchor point (10 ft).

Substituting the values in:

\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \] \[ c = \sqrt{500} \] \[ c \approx 22.4 \text{ ft} \]

Therefore, the length of the cable is approximately 22.4 ft.