1. **State the problem:** We are given the equation $g \sin 20^\circ = 7$ and need to find the value of $g$ to 2 decimal places. 2. **Formula and rules:** To isolate $g$, divide both sides of the equation by $\sin 20^\circ$. 3. **Isolate $g$:** $$g = \frac{7}{\sin 20^\circ}$$ 4. **Calculate $\sin 20^\circ$:** Using a calculator, $\sin 20^\circ \approx 0.34202$. 5. **Substitute and simplify:** $$g = \frac{7}{0.34202}$$ 6. **Perform the division:** $$g \approx 20.467$$ 7. **Round to 2 decimal places:** $$g \approx 20.47$$ **Final answer:** $g = 20.47$