Oscar uses a board to form a walking plank across a small ditch that has uneven sides. The board is 8 feet in length and stretches across the entire gap. The higher side is 3 feet above the other side. What is the approximate angle of elevation formed between the board and the lower side of the ditch?
To find the angle of elevation formed between the board and the lower side of the ditch, we can use the tangent function.
Let's consider the right triangle formed by the board as the hypotenuse, the height of the higher side of the ditch as the opposite side, and the distance across the ditch as the adjacent side.
Using the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = 3/8
Now, we can find the approximate angle by taking the arctangent (inverse tangent) of 3/8:
θ ≈ tan^(-1)(3/8) ≈ 20.56 degrees
Therefore, the approximate angle of elevation formed between the board and the lower side of the ditch is 20.56 degrees.