Question

a camper attaches a rope to the top of her tent to give it more support. she stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. about how tall is her tent? diagram options: 5.3 feet, 6 feet, 10 feet, 4.5 feet

Explanation:

Step1: Identify the triangle type

This is a right triangle problem, where the rope is the hypotenuse (\(c = 8\) ft), the distance from the middle of the tent to the stake is one leg (\(a = 6\) ft), and the height of the tent is the other leg (\(b\)). We use the Pythagorean theorem: \(a^2 + b^2 = c^2\).

Step2: Rearrange the formula for \(b\)

We solve for \(b\): \(b = \sqrt{c^2 - a^2}\)

Step3: Substitute the values

Substitute \(c = 8\) and \(a = 6\) into the formula: \(b = \sqrt{8^2 - 6^2} = \sqrt{64 - 36} = \sqrt{28}\)

Step4: Simplify \(\sqrt{28}\)

\(\sqrt{28} \approx 5.3\) (since \(5.3^2 \approx 28\))

Answer:

5.3 feet