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
500 ft.
500 ft.
22.4 ft.
22.4 ft.
300 ft.
300 ft.
17.3 ft.
17.3 ft.
Responses
500 ft.
500 ft.
22.4 ft.
22.4 ft.
300 ft.
300 ft.
17.3 ft.
17.3 ft.
Answers
GPT 3.5
22.4 ft.
could you work this out
GPT 3.5
Of course! We can solve this problem using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote:
- The height of the pole as x (20 ft.)
- The distance from the support cable attachment point on the pole to the base of the pole as y (10 ft.)
- The length of the cable as z
According to the Pythagorean theorem:
x² + y² = z²
20² + 10² = z²
400 + 100 = z²
500 = z²
z = sqrt(500)
z ≈ 22.4 ft.
Therefore, the length of the cable is approximately 22.4 ft.
Let's denote:
- The height of the pole as x (20 ft.)
- The distance from the support cable attachment point on the pole to the base of the pole as y (10 ft.)
- The length of the cable as z
According to the Pythagorean theorem:
x² + y² = z²
20² + 10² = z²
400 + 100 = z²
500 = z²
z = sqrt(500)
z ≈ 22.4 ft.
Therefore, the length of the cable is approximately 22.4 ft.