janelle is shooting free throws at a basetball hoop 9 feet off the ground. The hoop forms a 90 degree angle with the ground
The basketball hoop forms a right triangle with the ground. The height of the hoop is 9 feet, which is the length of the vertical side of the triangle. The angle between the ground and the hoop is 90 degrees, which is the right angle.
This means that the horizontal distance between Janelle and the base of the hoop is the base of the triangle. Let's call this distance "x".
Using the Pythagorean theorem, we can relate the height, base, and the hypotenuse of the triangle (which is the diagonal distance between Janelle and the hoop):
base^2 + height^2 = hypotenuse^2
x^2 + 9^2 = hypotenuse^2
We don't know the value of the hypotenuse, so we'll leave it as "h".
x^2 + 81 = h^2
So, we can see that the horizontal distance between Janelle and the base of the hoop is determined by the value of "h". The hypotenuse represents the total distance between Janelle and the hoop.
If Janelle is shooting free throws, it means she is standing at a certain distance away from the hoop. Let's say she is standing "d" feet away from the hoop horizontally.
Therefore, the total distance between Janelle and the hoop is: d + h
So, the horizontal distance between Janelle and the base of the hoop is x = d.
In summary, the horizontal distance between Janelle and the base of the hoop is d feet, while the vertical distance (height) is 9 feet.