Final answer:
To determine the length of the guy wire, subtract the height of the attachment point from the total height of the tower, use the tangent of the given angle to find the ground length, and then apply the Pythagorean theorem to find the length of the guy wire, which is approximately 388.24 feet.
Step-by-step explanation:
The question asks for the length of a guy wire for a radio transmission tower that has specific dimensions and angles. To solve this problem, we apply trigonometric principles, particularly the tangent function, because we are dealing with a right triangle formed by the height of the tower, the length of the guy wire, and the distance from the ground to the point where the guy wire is attached.The height of the tower where the wire is attached is 375.4 feet minus 15.2 feet, which equals 360.2 feet. The tangent of 56 degrees is equal to the opposite side (the height at which the wire is attached) divided by the adjacent side (the ground length from the tower to the stake). So, tangent(56 degrees) = 360.2 feet / ground length. We solve for the ground length and then use the Pythagorean theorem to find the length of the guy wire.
First, let's calculate the ground length: ground length = 360.2 feet / tangent(56 degrees), and then using a calculator, we estimate the lengthNext, we use the Pythagorean theorem: (Length of the guy wire)^2 = (360.2 feet)^2 + (ground length)^2After calculating those values, we find out that the guy wire's length is approximately option C) 388.24 feet.To find the length of the guy wire, we can use trigonometry. The guy wire forms a right triangle with the vertical pole and the ground. We can use the tangent function to find the length of the guy wire.First, we need to find the length of the side adjacent to the angle. We know that the height of the pole is 375.4 feet and the guy wire is attached 15.2 feet from the top. So the adjacent side is 375.4 - 15.2 = 360.2 feet.Next, we can use the tangent function to find the length of the guy wire. tan(56) = opposite/adjacent, where the opposite side is the length of the guy wire. So, tan(56) = opposite/360.2. Solving for the opposite side gives us the length of the guy wire, which is approximately 402.37 feet.