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? options: 6.9 feet, 12 feet, 4 feet, 8.9 feet (with a diagram of the tent showing a right triangle with height 4 ft and hypotenuse 8 ft)

Explanation:

Step1: Identify the triangle type

This is a right triangle where the rope is the hypotenuse (\(c = 8\) feet) and the height from the ground to the top of the tent is one leg (\(a = 4\) feet). We need to find the other leg (\(b\)) using the Pythagorean theorem \(a^2 + b^2 = c^2\).

Step2: Rearrange the formula

To solve for \(b\), we rearrange the formula: \(b = \sqrt{c^2 - a^2}\).

Step3: Substitute the values

Substitute \(a = 4\) and \(c = 8\) into the formula: \(b = \sqrt{8^2 - 4^2} = \sqrt{64 - 16} = \sqrt{48}\).

Step4: Simplify the square root

\(\sqrt{48} \approx 6.9\) (since \(6.9^2 \approx 47.61\) which is close to 48).

Answer:

6.9 feet