1. **State the problem:** Find the numerical value of $\sin 240^\circ + \sin 90^\circ - \cos 30^\circ$. 2. **Recall the values of trigonometric functions:** - $\sin 240^\circ = \sin(180^\circ + 60^\circ) = -\sin 60^\circ = -\frac{\sqrt{3}}{2}$ - $\sin 90^\circ = 1$ - $\cos 30^\circ = \frac{\sqrt{3}}{2}$ 3. **Substitute these values into the expression:** $$\sin 240^\circ + \sin 90^\circ - \cos 30^\circ = -\frac{\sqrt{3}}{2} + 1 - \frac{\sqrt{3}}{2}$$ 4. **Combine like terms:** $$1 - \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} = 1 - \sqrt{3}$$ 5. **Final answer:** $$\boxed{1 - \sqrt{3}}$$ This corresponds to option C.