Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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? image of tent, rope, and stake with 4 ft, 8 ft, and? options: 8.9 feet, 4 feet, 12 feet, 6.9 feet

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the height of the tent (4 feet) is one leg, the distance from the middle of the tent to the stake (let's call it \(x\)) is the other leg, and the rope (8 feet) is the hypotenuse. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs. Here, \(a = 4\), \(c = 8\), and we need to find \(b=x\).

Step2: Substitute values into the formula

Substitute \(a = 4\) and \(c = 8\) into the Pythagorean theorem: \(4^{2}+x^{2}=8^{2}\).
Calculate \(4^{2}=16\) and \(8^{2}=64\), so the equation becomes \(16 + x^{2}=64\).

Step3: Solve for \(x^{2}\)

Subtract 16 from both sides of the equation: \(x^{2}=64 - 16\).
\(64-16 = 48\), so \(x^{2}=48\).

Step4: Solve for \(x\)

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

Answer:

6.9 feet (corresponding to the option "6.9 feet")