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? 10 feet 6 feet 5.3 feet 4.5 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the rope, \(c = 8\) ft) and \(a\) is the base (distance from the tent, \(a=6\) ft), and \(b\) is the height of the tent. We need to solve for \(b\), so the formula becomes \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

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

Step3: Simplify the square root

\(\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\approx2\times2.65 = 5.3\) (since \(\sqrt{7}\approx2.65\)).

Answer:

5.3 feet