Question

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?
o 10 feet
o 6 feet
o 4.5 feet
o 5.3 feet
topic: the pythagorean theorem

Explanation:

Step1: Identify the right - triangle

The rope, the height of the tent, and the distance from the base of the tent to the stake form a right - triangle. The length of the rope is the hypotenuse ($c = 8$ feet) and the distance from the base of the tent to the stake is one of the legs ($a = 6$ feet). We want to find the other leg ($b$), which is the height of the tent.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 6$ and $c = 8$ into the formula: $b=\sqrt{8^{2}-6^{2}}=\sqrt{64 - 36}=\sqrt{28}\approx5.3$ feet.

Answer:

5.3 feet