calculate sine of 30 degrees using a right triangle

1. Identify the definition of sine: In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$

2. Locate the sides relative to the 30° angle: Looking at the provided triangle, for the angle $30^{\circ}$:
- The side opposite to the $30^{\circ}$ angle has a length of $1$.
- The hypotenuse (the side opposite the $90^{\circ}$ angle) has a length of $2$.

3. Calculate the sine value: Substitute the values into the sine formula:
$$\sin(30^{\circ}) = \frac{1}{2}$$

1. Compare with the given options: Comparing our result with the choices provided, it matches option E.