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?
To find the height of the tent, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) 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 with the distance from the middle of the tent to the stake (6 ft) as one of the other sides. Let h be the height of the tent.
Using the Pythagorean theorem:
(6)^2 + h^2 = (8)^2
36 + h^2 = 64
h^2 = 64 - 36
h^2 = 28
h = √28
h ≈ 5.29 ft
Therefore, the tent is approximately 5.29 feet tall.