Final answer:
The length of the tent pole can be calculated using the Pythagorean theorem as it forms a right-angled triangle with the ground and the guy rope. After performing the needed calculation, it is found that the closest length of the tent pole is about 7.3 feet.
Step-by-step explanation:
We can consider this to be a right-angled triangle problem, where the guy rope is the hypotenuse, the distance from the tent to the peg is one of the legs, and the tent pole is the other leg. By applying the Pythagorean theorem (a^2 + b^2 = c^2), where: 'a' is the length of the tent pole we're trying to find, 'b' is the distance the peg is from the tent (8 feet), 'c' is the length of the guy rope (11 feet). We get: a^2 + 8^2 = 11^2, So: a^2 + 64 = 121. Subtracting 64 from both sides gives us: a^2 = 121 - 64. Therefore: a^2 = 57. To find 'a', we take the square root of 57: ≈ 7.55 feet. The tent pole is therefore closest to the second option: b) The tent pole is about 7.3 feet long.