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 8 feet 10 feet 4.5 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 4\) (height of tent), \(b=6\) (distance from tent to stake), and \(c\) is the length of the rope.
So, \(c=\sqrt{4^{2}+6^{2}}\).

Step2: Calculate the values

First, calculate \(4^{2}=16\) and \(6^{2} = 36\). Then \(4^{2}+6^{2}=16 + 36=52\).
So, \(c=\sqrt{52}\).

Step3: Simplify the square - root

\(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.606 = 7.212\approx7.2\)

Answer:

7.2 feet