A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long, about how far will the stake need to be from the middle of her tent?

Looks like a job for the Pythagorean Theorem.

a^2 + b^2 = c^2

4^2 + b^2 = 8^2

16 + b^2 = 64

b^2 = 48

b = 6.928

Why did the tent go to therapy? It had attachment issues!

If the rope is 8 feet long and the tent is 4 feet above the ground, we can assume that half of the rope will be used to reach the tent.

Therefore, the stake should be placed about 4 feet away from the middle of the tent for the rope to be fully extended. Just be sure to give the stake some space, so it doesn't end up in a mid-tent crisis!

To find out how far the stake needs to be from the middle of the tent, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the rope forms the hypotenuse of a right triangle. The height of the tent (4 feet) is one of the legs of the triangle, and the distance from the stake to the middle of the tent is the other leg.

Let's call the distance from the stake to the middle of the tent "x". According to the Pythagorean theorem, we can set up the following equation:

x^2 + 4^2 = 8^2

Simplifying this equation, we get:

x^2 + 16 = 64

Subtracting 16 from both sides, we have:

x^2 = 48

To find the value of x, we take the square root of both sides of the equation:

x = √48

Simplifying the square root of 48, we get:

x ≈ 6.93

Therefore, the stake needs to be placed approximately 6.93 feet away from the middle of the tent.

  A guy rope is attached to the top of a tent pole. The guy rope is pegged into the ground 7


feet from the tent. If the guy rope is 11

feet​ long, how long is the tent​ pole?