Scott set up a volleyball net in his backyard. one of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 8 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope.

Thanks a lot Steve.

skrrt

To find the length of the rope, we can use the Pythagorean theorem since we have a right triangle. 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 lengths of the other two sides.

In this case, the pole forms the vertical side and the stake forms the horizontal side. Let's call the length of the rope "r". So, we have one side of length 6 feet (the height of the pole) and another side of length 8 feet (the distance from the bottom of the pole to the stake).

Using the Pythagorean theorem, we can write:

r^2 = 6^2 + 8^2

Simplifying this equation, we have:

r^2 = 36 + 64

r^2 = 100

To find the length of the rope, we need to take the square root of both sides:

r = √100

r = 10 feet

Therefore, the length of the rope is approximately 10 feet.

learn to recognize common Pythagorean triples in right triangles. The simplest is 3-4-5. This is just double that, or 6-8-10.

The rope is 10 feet long.

Or, you can do the algebra, using

r^2 = 6^2+8^2
and solve for r.