Question

perry wants to replace the net on his basketball hoop. The hoop is 10 feet high. Perry places his ladder 4 feet from the base of the hoop. How long must his ladder be to reach the hoop? Round your answer to the nearest hundredth

Answer 1

Perry's ladder must be approximately 10.77 feet long, calculated using the Pythagorean theorem, to reach the 10 feet high basketball hoop when placed 4 feet from the hoop's base.

Step-by-step explanation:

Perry needs to solve a right triangle problem to determine the length of the ladder he must use to reach the 10 feet high basketball hoop when placed 4 feet from the base. To solve this, we use the Pythagorean theorem which states that the square of the length of the hypotenuse (the side opposite the right angle, which in this case is the length of the ladder) is equal to the sum of the squares of the lengths of the other two sides.

In Perry's case, the two sides are 10 feet (height of the basketball hoop) and 4 feet (distance from the hoop). Let's denote the length of the ladder as 'L'. According to the Pythagorean theorem, we have:

L² = 10² + 4²

L² = 100 + 16

L² = 116

L = √116

L = 10.77 feet

Rounded to the nearest hundredth, Perry's ladder must be approximately 10.77 feet long to reach the hoop.

Answer 2

For this case we can model the problem as a rectangle triangle.
We have two sides of the triangle.
We must find the hypotenuse.
Using the Pythagorean theorem we have:
h = root ((10) ^ 2 + (4) ^ 2)
h = 10.77 feet
Answer:
his ladder must be 10.77 feet long to reach the hoop