Final answer:
The diagonal of a rectangle that is 20 meters wide and 30 meters long makes an approximate angle of 33.69 degrees with the length of the rectangle, calculated using tan(θ) = opposite/adjacent.
Step-by-step explanation:
The student is asking about the angle a diagonal of a rectangle makes with the length of the rectangle. To solve this, we use trigonometry; the angle can be found by using the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. Since the rectangle is 20m wide (opposite side) and 30m long (adjacent side), we can use the formula tan(θ) = opposite/adjacent, where θ is the angle we want to find. Using a calculator, we find that tan(θ) = 20/30 which gives θ ≈ 33.69 degrees. Thus, the diagonal makes an angle of approximately 33.69 degrees with the length of the rectangle.