Final answer:
The angle that the plank makes with the wall is approximately 29.74 degrees, which can be calculated using the inverse tangent function on the ratio of the wall's height to the length of the plank along the ground.
Step-by-step explanation:
The student is asking about the angle a plank makes with a wall when it is leaning against it. To find the angle that the 5m long plank makes with the wall that is 2m high, we can use trigonometric ratios. Specifically, we can use the tangent function which is the opposite side over the adjacent side in a right-angled triangle. Here, the opposite side is the height of the wall (2m), and the adjacent side would be the length of the plank along the ground, which can be found by subtracting the overhanging part of the plank (1.5m) from the total length of the plank (5m).
Thus, the length of the plank along the ground is 5m - 1.5m = 3.5m. The angle θ between the plank and the wall can be found using the equation tangent(θ) = opposite/adjacent, or tan(θ) = 2/3.5. To find the angle θ, you would perform the inverse tangent function (arctan) of the ratio (2/3.5).
To calculate the angle: θ = arctan(2/3.5). Using a calculator, the angle θ comes out to be approximately 29.74 degrees.