Question

Oscar uses a board to form a walking plank across a small ditch that has uneven sides. The board is 8 ft in length and stretches across the entire gap. The higher side of the gap is 3 ft higher than the other side. What is the approximate angle of elevation formed between the board and the lower side of the ditch? Round your answer to the nearest whole number. (no decimals)





(1 point)
The angle of elevation is
degrees

Answer 1

To find the angle of elevation formed between the board and the lower side of the ditch, we can use some trigonometry.

In this scenario, we can imagine a right triangle where:
- The length of the board (the hypotenuse) is 8 ft.
- The height difference between the two sides of the ditch (the opposite side) is 3 ft.
- The adjacent side can be calculated using the Pythagorean theorem.

The relationship we can use to find the angle θ (the angle of elevation) is given by the sine function:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{8}
\]

Now, we will calculate the angle θ:

\[
\theta = \arcsin\left(\frac{3}{8}\right)
\]

Using a calculator to find the angle:

\[
\theta \approx 22.03 \text{ degrees}
\]

Rounding to the nearest whole number, we find:

\[
\theta \approx 22 \text{ degrees}
\]

Thus, the angle of elevation is

\[
\boxed{22} \text{ degrees}
\]