A guy wire is attached to a tower at a point that is 5.5m above the ground. The angle between the wire and the level ground is 56 degrees. How far from the base of the tower is the wire anchored to the ground, to the nearest tenth of a metre?

tan theta = 5.5 / d

To find the distance from the base of the tower to where the wire is anchored on the ground, we can use trigonometry. We'll use the tangent function in this case.

Let's consider the right-angled triangle formed by the tower, the wire, and the ground. The vertical side of the triangle represents the height of the tower and is given as 5.5m. The angle between the wire and the ground is 56 degrees.

Using the tangent function, we can write the equation:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the tower (5.5m), and we need to find the adjacent side (the distance from the base of the tower to where the wire is anchored on the ground).

So, we can rearrange the equation to solve for the adjacent side:

adjacent = opposite/tan(angle)

Plugging in the values:

adjacent = 5.5m / tan(56 degrees)

Calculating this, we find:

adjacent ≈ 5.5m / 1.504

adjacent ≈ 3.656m

Therefore, the wire is anchored approximately 3.7 meters away from the base of the tower.