Question

topic: the pythagorean theorem
progress:
question id: 109878
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
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?
4.5 feet
5.3 feet
10 feet
6 feet

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse of a right - triangle and $a$ and $b$ are the other two sides. In this case, the length of the rope is the hypotenuse $c = 8$ ft and the distance from the middle of the tent to the stake is one side $a = 6$ ft. We want to find the height of the tent $b$.

Step2: Rearrange the formula

We can rewrite the Pythagorean theorem to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $c = 8$ and $a = 6$ into the formula: $b=\sqrt{8^{2}-6^{2}}=\sqrt{64 - 36}=\sqrt{28}$.

Step4: Simplify the square - root

$\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\approx2\times2.65 = 5.3$ ft.

Answer:

5.3 feet