- Identify the trigonometric ratio: The problem asks for the sine of an angle. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
- Identify the angle: The angle in question is $28^\circ$.
- Identify the side opposite the angle: In the given diagram, the side opposite the $28^\circ$ angle has a length of 8.
- Identify the hypotenuse: The hypotenuse is the longest side of the right-angled triangle, which is opposite the right angle ($90^\circ$). In this diagram, the hypotenuse has a length of 17.
5. Calculate the sine: Using the definition of sine, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$:
$$\sin(28^\circ) = \frac{8}{17}$$