A camper attaches a rope from the top of her tent,
feet above the ground, to give it more support. If she stakes the rope to the ground
feet from the middle of her tent, about how long is the rope from the ground to the tent?
An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is 4 feet. The base of the triangle is 6 feet. The hypotenuse is unknown.
A) 4.5 feet
B) 7.2 feet
C) 8 feet
D) 10 feet
To find the length of the hypotenuse (the rope from the ground to 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 length of the height of the triangle is 4 feet and the length of the base is 6 feet. So, we can use the Pythagorean theorem to find the length of the hypotenuse:
Hypotenuse^2 = Height^2 + Base^2
Hypotenuse^2 = 4^2 + 6^2
Hypotenuse^2 = 16 + 36
Hypotenuse^2 = 52
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = √52
Hypotenuse ≈ 7.2 feet
Therefore, the length of the rope from the ground to the tent is approximately 7.2 feet.
The correct answer is B) 7.2 feet.