Final answer:
The correct option: 90.0 meters.
To find the length of the guy wire, we can use trigonometry. By taking the tangent of the given angle (converted to decimal format) and relating it to the height of the tower, we solve for the hypotenuse. The calculated length of the guy wire is approximately 90.0 meters.
Step-by-step explanation:
The question asks us to find the length of a guy wire that makes an angle of 45 degrees 30 minutes with the ground and is attached to the top of a tower that is 63.9 meters high. Using trigonometry, specifically the tangent function which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side, we can solve this problem. As we are dealing with an angle not in pure degrees, we will first convert 45 degrees 30 minutes to a decimal by realizing that 30 minutes is equal to 0.5 degrees.
Therefore, the angle in decimal format is 45.5 degrees. In the right triangle formed, the height of the tower is the opposite side (63.9 m), and we need to find the hypotenuse which is the length of the guy wire. By taking the tangent of 45.5 degrees and equating it to the opposite over the adjacent (height over length), we have:
tan(45.5°) = 63.9 / length
We then solve for the length of the guy wire:
length = 63.9 / tan(45.5°)
The calculation gives us the precise length of the guy wire required to reach the top of the tower from the ground at the given angle. After performing this calculation, the closest match from the options provided is B) 90.0 m.