Use the Pythagorean Theorem Quick Check

Question

4 of 54 of 5 Items

Question
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)
Responses

300 ft.
300 ft.

17.3 ft.
17.3 ft.

22.4 ft.
22.4 ft.

500 ft.
500 ft.
Skip to navigation

Answer 1

To find the length of the cable, we can use the Pythagorean Theorem, which 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). The formula is:

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

In this scenario, we can define:

• \( a = 20 \) ft (the height of the pole where the cable is attached)
• \( b = 10 \) ft (the distance from the base of the pole to where the cable is anchored)

Now, we can apply the Pythagorean Theorem:

1. Calculate \( a^2 \) and \( b^2 \):

   • \( a^2 = 20^2 = 400 \)
   • \( b^2 = 10^2 = 100 \)

2. Add \( a^2 \) and \( b^2 \): \[ c^2 = a^2 + b^2 = 400 + 100 = 500 \]

3. Take the square root of both sides to find \( c \): \[ c = \sqrt{500} \approx 22.4 \]

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

So the correct answer is 22.4 ft.