Final answer:
The height of the camper's tent is calculated using the Pythagorean theorem, forming a right-angled triangle with the rope as the hypotenuse and the tent's height as one leg. After computation, the tent is found to be approximately 5.3 feet tall, corresponding to option B.
Step-by-step explanation:
The question asks us to determine the height of a tent when a camper has attached a rope for support. This scenario forms a right-angled triangle with the rope as the hypotenuse, the distance from the tent to where the rope is staked as one leg, and the tent's height as the other leg. To solve this, we can use the Pythagorean theorem which states that in a right-angled triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
The formula is a2 + b2 = c2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. We know that the rope (hypotenuse c) is 8 ft long and the distance from the tent to the stake (one leg a) is 6 ft. We need to solve for the tent's height (other leg b).
Accordingly, we square the lengths of the rope and the distance: 82 = 64 and 62 = 36. We then subtract the square of distance from the square of the rope length to find the square of the tent's height: 64 - 36 = 28. Therefore, the tent's height (b) will be the square root of 28, which is approximately 5.3 feet. This corresponds to option B.