Answer:
Let's denote the horizontal distance of the support beam from the bottom of the ladder as "x" meters.
According to the given information, the ladder is resting against a vertical wall that is 1.8m high, and the support beam is placed 0.6m away from the wall. The length of the support beam is 0.6m.
We can use similar triangles to solve for "x". The triangles formed by the ladder, the support beam, and the vertical wall are similar triangles.
The height of the vertical wall (1.8m) corresponds to the length of the ladder along the wall, and the horizontal distance from the wall to the support beam (0.6m) corresponds to "x" meters on the ladder.
Using the concept of similar triangles, we can set up the following proportion:
(Height of wall) / (Horizontal distance from wall to support beam) = (Length of ladder) / (Distance from bottom of ladder to support beam)
Plugging in the given values:
1.8 / 0.6 = (Length of ladder) / x
Simplifying the proportion:
3 = (Length of ladder) / x
To find the length of the ladder, we can use the Pythagorean theorem, which states that the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (height of wall and horizontal distance from wall to support beam).
Length of ladder = √(height of wall)^2 + (horizontal distance from wall to support beam)^2
Length of ladder = √(1.8)^2 + (0.6)^2
Length of ladder = √3.24 + 0.36
Length of ladder = √3.6
Length of ladder ≈ 1.897 m (rounded to three decimal places)
Plugging this value back into the proportion:
3 = 1.897 / x
Solving for "x":
x = 1.897 / 3
x ≈ 0.632 m (rounded to three decimal places)
So, the horizontal distance of the support beam from the bottom of the ladder is approximately 0.632 meters.