To secure a 500 m radio tower against Highwinds Guy wires are attached to the top of the tower. Each wire forms is 75° angle with the top of the tower find the length of the wire from the tower to its anchor in the ground.
To find the length of the guy wire from the tower to its anchor in the ground, we can use trigonometry.
Let's denote the length of the guy wire as "x".
We can use the angle of 75° and the height of the tower, which is 500 m, to find x.
In a right triangle formed by the guy wire, the height of the tower, and the distance from the tower to the anchor in the ground, the angle of 75° is opposite the height of the tower.
From trigonometry, we know that the cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is the height of the tower (500 m), and the hypotenuse is the length of the guy wire (x).
Therefore, we have cos(75°) = 500 m / x.
To find the length of the guy wire, we can rearrange this equation to solve for x.
x = 500 m / cos(75°).
Using a calculator, we can evaluate this expression.
x ≈ 500 m / 0.2588 ≈ 1930.83 m.
Therefore, the length of the guy wire from the tower to its anchor in the ground is approximately 1930.83 meters.