A 30-foot cable is suspended between the tops of two 20-foot poles on level ground. The lowest point of the cable is 5 feet above the ground. What is the distance between the two poles?
0' (zero feet)
15' down plus 15' straight back up is 30'. There can be no allowance for horizontal distance. The poles must be co-located.
To find the distance between the two poles, you can use the Pythagorean Theorem.
Let's call the distance between the two poles "x".
Using the Pythagorean Theorem, we have:
x^2 = (20)^2 + (30-5)^2
Simplifying the equation:
x^2 = 400 + 625
x^2 = 1025
Taking the square root of both sides:
x = √1025
x ≈ 32.01 feet
Therefore, the distance between the two poles is approximately 32.01 feet.
To find the distance between the two poles, we can use the Pythagorean theorem.
Let's consider a right-angled triangle formed by the cable, the ground, and a line connecting the lowest point of the cable to the ground. The distance between the two poles is the horizontal distance between the points where the cable meets the poles.
The length of the cable represents the hypotenuse of the right-angled triangle, which is 30 feet. One of the legs is the distance from the lowest point of the cable to the ground, which is 5 feet. Let's call the length of the other leg (the horizontal distance between the two poles) "x."
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse (the cable), a is the length of one leg (the distance from the lowest point to the ground), and b is the length of the other leg (the distance between the poles).
Substituting in the given values:
30^2 = 5^2 + x^2
Simplifying:
900 = 25 + x^2
Subtracting 25 from both sides:
875 = x^2
Finally, taking the square root of both sides to isolate x:
x = sqrt(875)
Using a calculator, we find that:
x ≈ 29.58 feet
Therefore, the distance between the two poles is approximately 29.58 feet.