1. The problem asks to evaluate $2.14 \sin 75^\circ$ and round the answer to 2 decimal places. 2. Recall that $\sin 75^\circ$ is the sine of 75 degrees. 3. Use a calculator or sine tables to find $\sin 75^\circ \approx 0.9659$. 4. Multiply $2.14$ by $0.9659$: $$2.14 \times 0.9659 = 2.066226$$ 5. Round $2.066226$ to 2 decimal places to get $2.07$. Final answer: $2.07$