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)

Question

Responses

30
30

29
29

15
15

31

Answer 1

To find the angle of elevation formed between the board and the lower side of the ditch, we can use the inverse sine function.

Here's how we can set it up:

1. Let \( L \) be the length of the board, which is 6 feet.
2. Let \( h \) be the height difference between the two sides of the ditch, which is 3 feet.
3. When Oscar places the board, it creates a right triangle where:
   • The height (opposite side) is 3 feet,
   • The hypotenuse (the board) is 6 feet.

We can use the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L} = \frac{3}{6} = \frac{1}{2}. \]

Now, to find the angle \( \theta \):

\[ \theta = \sin^{-1}\left(\frac{1}{2}\right). \]

The angle whose sine is \( \frac{1}{2} \) is \( 30^\circ \).

Thus, the approximate angle of elevation formed between the board and the lower side of the ditch is:

30 degrees.