A tether ball is attached to the top of a 15-foot pole. Maddy holds the ball 3 feet off the ground and 4 feet from the pole. How long is the rope that the tether ball is attached to?
160 ft
160
To find the length of the rope that the tether ball is attached to, we can use the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
In this case, we have a right triangle formed by the pole, the rope, and the distance from the pole to where Maddy holds the ball. Let's call the length of the rope x.
Using the Pythagorean theorem, we have:
x^2 = 4^2 + 15^2
Simplifying, we get:
x^2 = 16 + 225
x^2 = 241
Taking the square root of both sides of the equation, we find:
x = sqrt(241)
So, the length of the rope that the tether ball is attached to is approximately sqrt(241) feet.
vertical = 15 -3 = 12
horizontal = 4
hypotenuse^2 = 4^2 + (4*3)^2 = 4^2 + 9 *4^2 = 10 * 4^2
so hypotenuse = 4 sqrt 10