Question

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? (1 point)

Answer 1

To find the angle of elevation between the board and the lower side of the ditch using the inverse sine function, we can set up the problem using the given dimensions.

1. **Identify the sides of the triangle**:
- The length of the board (hypotenuse) = 6 feet.
- The vertical height (opposite side) = 3 feet (the difference in height between the two sides of the ditch).

2. **Use the sine definition**:
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{6} = \frac{1}{2}
\]

3. **Find the angle using the inverse sine**:
To find the angle \(\theta\), we take the inverse sine (or arcsin) of \(1/2\):
\[
\theta = \sin^{-1}\left(\frac{1}{2}\right)
\]

4. **Calculate the angle**:
The angle whose sine is \(1/2\) is \(30^\circ\).

Therefore, the approximate angle of elevation formed between the board and the lower side of the ditch is **30 degrees**.