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. the minimum length of the slanted poles needed to support the fly is feet. type the correct answer in the box. write your answer to two decimal places.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 12\) (height of the fly), \(b=\frac{16}{2}=8\) (half - width of the base, since the poles are symmetrically placed).

$$c=\sqrt{12^{2}+8^{2}}$$

Step2: Calculate the values

First, calculate \(12^{2}=144\) and \(8^{2}=64\). Then \(12^{2}+8^{2}=144 + 64=208\).

$$c=\sqrt{208}$$

Step3: Simplify the square root

We can rewrite \(208\) as \(16\times13\). So \(\sqrt{208}=\sqrt{16\times13}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 16\), \(b = 13\)), we get \(\sqrt{16}\times\sqrt{13}=4\sqrt{13}\approx4\times3.606 = 14.42\)

Answer:

\(14.42\)