Question

a camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. if the rope is 8 feet long, about how far will the stake need to be from the middle of her tent? 6.9 feet 12 feet 4 feet 8.9 feet

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the rope, \(c = 8\) feet) and \(a\) is one - leg (height of the tent, \(a=4\) feet). Let \(b\) be the distance from the stake to the middle of the tent. We need to solve for \(b\).

$$b^{2}=c^{2}-a^{2}$$

Step2: Substitute the values

Substitute \(a = 4\) and \(c = 8\) into the formula:

$$b^{2}=8^{2}-4^{2}$$

$$b^{2}=64 - 16$$

$$b^{2}=48$$

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{48}\)
Simplify \(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\approx4\times1.732 = 6.928\approx6.9\)

Answer:

6.9 feet