__ 4.Brett needs to support a radio tower with guy wires. Each guy wire must run from the top of the tower to its own anchor 9 .00 m from the base of the tower. When the tower casts a shadow that is 9.00 m long, Brett's shadow is 0.60 m long. Brett is 1.85 m tall.What is the length of each guy wire that Brett needs? Comm 16

## Step 1: Finding the tower's height<br /><br />### Since Brett's height and shadow length are proportional to the tower's height and shadow length, we can set up a proportion: $\frac{\text{Tower's height}}{\text{Tower's shadow}} = \frac{\text{Brett's height}}{\text{Brett's shadow}}$. This gives us $\frac{h}{9.00} = \frac{1.85}{0.60}$. Solving for $h$, we get $h = \frac{1.85 \times 9.00}{0.60} = 27.75$ meters.<br /><br />## Step 2: Applying the Pythagorean theorem<br /><br />### The guy wire, the tower, and the ground form a right triangle. The tower's height is one leg (27.75 m), the distance from the base to the anchor is the other leg (9.00 m), and the guy wire is the hypotenuse. Using the Pythagorean theorem ($a^2 + b^2 = c^2$), we have $27.75^2 + 9.00^2 = c^2$. This simplifies to $770.0625 + 81 = c^2$, so $c^2 = 851.0625$. Taking the square root of both sides gives $c = \sqrt{851.0625} \approx 29.17$ meters.