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

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

• One leg (the vertical height from the ground to the point where the cable is attached on the pole) is 20 ft.
• The other leg (the horizontal distance from the base of the pole to the anchor point on the ground) is 10 ft.
• The hypotenuse (the length of the cable) is what we want to find.

According to the Pythagorean theorem:

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

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

Substituting the values:

\[ c^2 = 20^2 + 10^2 \] \[ c^2 = 400 + 100 \] \[ c^2 = 500 \]

Taking the square root of both sides:

\[ c = \sqrt{500} \approx 22.36 \]

Rounding to the nearest tenth:

\[ c \approx 22.4 \text{ ft.} \]

Thus, the length of the cable is 22.4 ft.