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 4.5 feet 10 feet

Explanation:

Step1: Apply Pythagorean theorem

The height of the tent \( h = 4\) feet and the horizontal distance \( b=6\) feet. The length of the rope \( l\) is the hypotenuse of a right - triangle. According to the Pythagorean theorem \(l^{2}=h^{2}+b^{2}\).
So, \(l^{2}=4^{2}+6^{2}\).

Step2: Calculate \(h^{2}+b^{2}\)

\(4^{2}=16\) and \(6^{2}=36\). Then \(l^{2}=16 + 36=52\).

Step3: Find \(l\)

\(l=\sqrt{52}\). Since \(\sqrt{49}<\sqrt{52}<\sqrt{64}\), and \(\sqrt{52}\approx7.21\) (because \(7.21^{2}=(7 + 0.21)^{2}=49+2\times7\times0.21 + 0.0441=49 + 2.94+0.0441 = 51.9841\approx52\)).

Answer:

7.2 feet