1. Problem: Given $A=49.7^\circ$ and $B=67.2^\circ$, we need to find $\cos 3A + \sin B$, rounded to three decimal places. 2. Calculate $3A$: $$3A = 3 \times 49.7^\circ = 149.1^\circ$$ 3. Evaluate $\cos 3A = \cos 149.1^\circ$ and $\sin B = \sin 67.2^\circ$ using a calculator: $$\cos 149.1^\circ \approx -0.864$$ $$\sin 67.2^\circ \approx 0.922$$ 4. Add the two values: $$\cos 3A + \sin B = -0.864 + 0.922 = 0.058$$ 5. The result rounded to three decimal places is: $$0.058$$