Question

a camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. if she stakes the rope to the ground 6 feet from the middle of her tent, about how long is the rope from the ground to the tent? 7.2 feet 4.5 feet 8 feet 10 feet

Explanation:

Step1: Apply Pythagorean theorem

The situation forms a right - triangle. Let the height of the tent be \(a = 4\) feet (one leg) and the distance from the middle of the tent to the stake be \(b=6\) feet (another leg). The length of the rope \(c\) is the hypotenuse. The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

Substitute \(a = 4\) and \(b = 6\) into the formula: \(c=\sqrt{4^{2}+6^{2}}=\sqrt{16 + 36}=\sqrt{52}\).

Step3: Simplify

\(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.61 = 7.22\approx7.2\) feet.

Answer:

A. 7.2 feet