Question

Jaclynn is building a cat house for her cats. She designs a ramp from one level to the other for them to climb. The ramp length is 4 ft and the difference between the two levels is 2 feet. What is the approximate angle of elevation formed by the ramp? Round your answer to the nearest whole number (no decimals)

Answer 1

To find the angle of elevation formed by the ramp, we can use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse.

1. **Define the triangle**:
- The ramp is the hypotenuse, which measures 4 ft.
- The difference in height between the two levels is the opposite side, which is 2 ft.
- The adjacent side is not needed for this calculation.

2. **Use the sine function**:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{2}{4} = 0.5
\]

3. **Find the angle**:
Now we need to find the angle \(\theta\) such that \(\sin(\theta) = 0.5\). Using a calculator or trigonometric tables, we find:
\[
\theta = \arcsin(0.5)
\]

4. **Calculate the angle**:
The angle whose sine is 0.5 is \(30^\circ\).

5. **Round to the nearest whole number**:
Since \(30\) is already a whole number, it remains \(30\).

Therefore, the approximate angle of elevation formed by the ramp is \(\boxed{30}\) degrees.