Question

A youth group is setting up camp. Rain is predicted, so the campers decide to build a fly, or rain cover, over their tent. The fly will be 12 feet high and 16 feet wide. The scouts are building the frame for the fly with two poles slanted and joined together at the top of the tent. What is the minimum length of slanted poles needed to support the fly

Answer 1

Answer: To find the length of the slanted poles, we need to solve a right triangle problem. The triangle's base is half of the width of the tent and its height is the height of the tent.

Given:

Height (h) = 12 feet

Width (w) = 16 feet / 2 = 8 feet

We apply the Pythagorean theorem, a² + b² = c², where a and b are the two sides of the right triangle (base and height), and c is the hypotenuse (the slanted pole in this case).

So, c² = h² + w²

c² = (12 ft)² + (8 ft)²

c² = 144 ft² + 64 ft²

c² = 208 ft²

c = √208 ft²

Taking the square root of 208 gives the length of the pole:

c ≈ 14.42 feet

So, the minimum length of slanted poles needed to support the fly is approximately 14.42 feet.