A circus performer walks on a tightrope 25 ft above the ground. The tightrope is supported by two beams and two support cables. If the distance between each beam and base of its support cable is 15 ft, what is the length of the support cable?
To find the length of the support cable, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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.
In this case, we can consider the support cable as the hypotenuse, and the distance between each beam and the base of the support cable as the other two sides.
Let's denote the length of the support cable as "c," and the length of the other two sides as "a" and "b."
According to the given information, we have:
a = 15 ft
b = 15 ft
Using the Pythagorean theorem, we can write:
c^2 = a^2 + b^2
Substituting the values:
c^2 = 15^2 + 15^2
c^2 = 225 + 225
c^2 = 450
To find the length of the support cable, we need to take the square root of both sides:
c = √450
c ≈ 21.21 ft
Therefore, the length of the support cable is approximately 21.21 ft.