Final answer:
The lower end of the support beam should be placed approximately 3.0 meters from the vertical beam, calculated using the tangent function of the 28° angle of elevation and the 1.6-meter height of the beam above the horizontal floor.
Step-by-step explanation:
To determine how far from the vertical beam the lower end of the support beam should be placed along the horizontal floor, we can use trigonometry. The scenario described forms a right-angled triangle where the height of the vertical beam represents the opposite side (1.6 meters), and the angle of elevation is given as 28°.
The length along the floor from the vertical beam to the support beam's lower end is the adjacent side of the right-angled triangle. We use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle:
tangent(angle) = opposite/adjacent
Therefore, to find the adjacent side (which is the distance from the vertical beam), we can rearrange the formula:
adjacent = opposite / tangent(angle)
Plugging in the values we get:
adjacent = 1.6 meters / tangent(28°)
Using a calculator, we find that:
adjacent ≈ 1.6 meters / 0.5317
adjacent ≈ 3.009 meters
The closest value to this calculation from the options is 3.0 meters, so the lower end of the support beam should be placed 3.0 meters from the vertical beam.