Oscar uses a board to form a walking plank across a small ditch that has uneven sides. The board is 6 feet in length and stretches across the entire gap. The higher side of the ditch is 3 feet above the other side. Using the inverse of sine, what is the approximate angle of elevation formed between the board and the lower side of the ditch?
To find the angle of elevation, we can use the inverse sine function.
Let x be the angle of elevation. We have the opposite side as 3 feet (the height difference between the two sides of the ditch) and the hypotenuse as 6 feet (the length of the board).
Using the formula for sine, we have sin(x) = opposite/hypotenuse = 3/6 = 1/2.
Taking the inverse sine of both sides, we have x = sin^(-1)(1/2).
Using a calculator, we find that sin^(-1)(1/2) is approximately 30 degrees.
Therefore, the approximate angle of elevation formed between the board and the lower side of the ditch is 30 degrees.