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?

Answer 1

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.