Question

Janelle is shooting free throws at a basketball hoop 9 feet off the ground. The hoop forms a 90 degree angle with the ground and she is standing 6 feet away. The diagram below shows a right triangle formed between Jenelle and the basketball hoop. The hypotenuse of a right triangle represents the side opposite the 90 degree angle. The length of that hypotenuse, represented by c can be found using the formula c^2=a^2 +b^2. find the length of the hypotenuse, which represents the shortest distance between jenelle and the hoop, in simplified form.

Answer 1

Using the given information, we can label the sides of the right triangle:
a = 6 feet (distance between Janelle and the hoop on the ground)
b = 9 feet (height of the hoop from the ground)

We can use the Pythagorean theorem to find the length of the hypotenuse (c):
c^2 = a^2 + b^2
c^2 = (6 feet)^2 + (9 feet)^2
c^2 = 36 feet^2 + 81 feet^2
c^2 = 117 feet^2

Taking the square root of both sides to find c, the length of the hypotenuse:
c = √(117 feet^2)
c = √(9 * 13 feet^2)
c = √(9) * √(13) * feet
c = 3 * √(13) * feet

Therefore, the length of the hypotenuse (shortest distance between Janelle and the hoop) is 3√(13) feet.