A theater is building a portable ramp to allow equimpment and people easy access to the stage, which is 2 meters high. If the ramp is 4 meters long, what is the angle of the incline in degrees ?

Answer

To find the angle of incline of the ramp, we can use trigonometric ratios. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Triangle**:
We have a right triangle formed by the ramp, the height of the stage, and the horizontal distance from the base of the ramp to the stage. The height of the stage (opposite side) is 2 meters, and the length of the ramp (hypotenuse) is 4 meters.

2. **Use the Sine Function**:
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can write:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{2}{4} \]

3. **Simplify the Ratio**:
Simplifying the ratio gives:
\[ \sin(\theta) = \frac{1}{2} \]

4. **Find the Angle**:
To find the angle \(\theta\), we take the inverse sine (also known as arcsin) of \(\frac{1}{2}\):
\[ \theta = \sin^{-1}\left(\frac{1}{2}\right) \]

5. **Calculate the Angle**:
From trigonometric tables or a calculator, we know that:
\[ \theta = 30^\circ \]

### Final Answer:
The angle of incline of the ramp is \(30^\circ\).

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