Question

A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent?

Answer 1

To find the height of the tent, the Pythagorean theorem is used with the tent's rope length and the distance it is staked from the tent, revealing the tent is approximately 5.29 feet tall.

Step-by-step explanation:

The question involves using the Pythagorean theorem to solve for the height of the tent. Given that the rope is 8 ft long (the hypotenuse of a right triangle) and it is staked to the ground 6 feet away from the tent (one of the legs), we can find the other leg, which represents the height of the tent. Using the Pythagorean theorem (a2 + b2 = c2), we substitute the known values to solve for the height (h) of the tent.

So the equation becomes h2 + 62 = 82.

Solving for h, we get: h2 = 82 - 62 = 64 - 36 = 28. Therefore h = √28, which is approximately 5.29 feet. So, the tent is about 5.29 feet tall.

Answer 2

5.3

Step-by-step explanation:

8^2 - 6^2 = x^2

64 - 36 = x^2

28 = x^2

Square root of 28 is approx 5.3