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 8.9 feet 4 feet 12 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the stake to the middle of the tent be \(x\). We have a right - triangle where the height of the tent (\(a = 4\) feet) is one leg, the distance \(x\) is the other leg, and the rope length (\(c=8\) feet) is the hypotenuse. According to the Pythagorean theorem \(a^{2}+x^{2}=c^{2}\), so \(x^{2}=c^{2}-a^{2}\).
Substitute \(a = 4\) and \(c = 8\) into the formula: \(x^{2}=8^{2}-4^{2}\).

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Step2: Solve for \(x\)

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

Answer:

6.9 feet