A guy wire is attached to the top of a 75 meter tower & meets the ground at a 65 degree angle. How long is the wire?
To find the length of the guy wire, we can use trigonometry. Specifically, we can use the trigonometric function tangent.
First, let's consider the triangle formed by the tower, the guy wire, and the ground. The side of the triangle opposite to the 65-degree angle is the length of the guy wire, and the side adjacent to the 65-degree angle is the height of the tower.
Using the tangent function, we can set up the equation:
tan(65 degrees) = height of the tower / length of the guy wire
Now, we can rearrange the equation to solve for the length of the guy wire:
length of the guy wire = height of the tower / tan(65 degrees)
Given that the height of the tower is 75 meters, we can substitute this value into the equation:
length of the guy wire = 75 meters / tan(65 degrees)
Calculating the result:
length of the guy wire ≈ 75 meters / 2.1445
Thus, the length of the guy wire is approximately 34.95 meters.