3.
Jaime is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 6.5 feet tall, and Jaime stakes the ropes into the ground 4 feet from the center of the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot?
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We can use the Pythagorean Theorem to find the length of one of the nylon ropes. Let's call the distance from the center of the tent to one of the stakes x. Then, the length of one of the nylon ropes (which we'll call L) is:
L^2 = x^2 + 6.5^2
L^2 = 16.25 + x^2
To find x, we can use the fact that the distance from the center of the tent to one of the stakes is 4 feet. We can imagine a right triangle with the tent being the hypotenuse, and the distance from the center of the tent to one of the stakes being one of the legs. Using the Pythagorean Theorem again:
4^2 + x^2 = 6.5^2
16 + x^2 = 42.25
x^2 = 26.25
x ≈ 5.1 feet (rounded to one decimal place)
Now that we know x, we can use the previous equation to find L:
L^2 = 16.25 + (5.1)^2
L^2 = 41.41
L ≈ 6.4 feet (rounded to one decimal place)
Since Jaime is using two nylon ropes, the total length of nylon rope he will use is:
2L ≈ 12.8 feet (rounded to one decimal place)