1. **State the problem:** We need to calculate the length $b$ in the given triangle, where one side is 23 mm and angles are given as 34°, 48°, 97°, and 102°. 2. **Analyze the triangle:** The base side is 23 mm with an adjacent angle of 34°. The triangle is divided inside, and the vertical side $b$ is opposite to the 34° angle. 3. **Use the Law of Sines:** The Law of Sines states: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, $c$ are sides opposite angles $A$, $B$, $C$ respectively. 4. **Identify known values:** - Side $a = 23$ mm opposite angle $A = 48^\circ$ (since the 23 mm side is opposite the 48° angle in the smaller triangle). - Angle $B = 34^\circ$ opposite side $b$ (the length we want). 5. **Apply Law of Sines to find $b$:** $$b = a \times \frac{\sin B}{\sin A} = 23 \times \frac{\sin 34^\circ}{\sin 48^\circ}$$ 6. **Calculate sine values:** $$\sin 34^\circ \approx 0.5592$$ $$\sin 48^\circ \approx 0.7431$$ 7. **Calculate $b$:** $$b = 23 \times \frac{0.5592}{0.7431} = 23 \times 0.7529 = 17.3167$$ 8. **Round to 3 significant figures:** $$b \approx 17.3 \text{ mm}$$ **Final answer:** $$\boxed{17.3 \text{ mm}}$$