A radio transmission tower is 471.0 feet tall. A guy wire is to be attached 6 feet from the top and is to make an angle of 23.1 degrees with the ground? How many feet long should the guy wire be? I am confused on how to find the equation for this problem so that I may work it out.

To solve this problem, we can use trigonometric concepts. Let's break it down step by step:

Step 1: Visualize the situation
Imagine the radio transmission tower standing upright. We know the height of the tower is 471.0 feet. A guy wire is attached 6 feet from the top, forming an angle of 23.1 degrees with the ground. We need to find the length of the guy wire, which we'll call "d".

Step 2: Use trigonometry to relate the height, the guy wire, and the angle
Since we have a right triangle formed by the tower, the ground, and the guy wire, we can use trigonometric ratios. In this case, we can use the tangent function since we have the opposite (the height) and the adjacent (the distance from the top to the point where the guy wire is attached).

The tangent of an angle is defined as:

tan(angle) = opposite / adjacent

In this case, the angle is 23.1 degrees, the adjacent side is 6 feet, and we want to find the opposite side (the length of the guy wire, denoted as "d").

So, we can rearrange the formula to solve for "d":

d = opposite / tan(angle)

Step 3: Plug in the values and calculate
Now, we can substitute the values into the equation:

d = 471.0 feet / tan(23.1 degrees)

Using a scientific calculator:

d ≈ 1078.03 feet

Therefore, the guy wire should be approximately 1078.03 feet long.

Remember to double-check your units and make sure they are consistent throughout the calculation.

The 6 feet at the top is just noise, placed there to see whether you know how to subtract.

The wire is attached 465 feet from the ground. So, you have a right triangle with an angle of 23.1° opposite the pole. (assuming the pole is vertical)

Checking your basic trig definitions, if the length of wire is x, then

465/x = sin 23.1°