To solve for angle $BAC$ using the Sine Rule, let's break it down:

The Sine Rule states:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Step-by-step Solution:

1. Identify sides and angles:

   • Side $BC = 14 \, \text{m}$,
   • Side $AB = 20 \, \text{m}$,
   • Angle $BCA = 43^\circ$.

2. Apply the Sine Rule: To find $\angle BAC$, we first calculate $\sin BAC$: $\frac{\sin BAC}{BC} = \frac{\sin BCA}{AB}$

   Substituting the known values: $\frac{\sin BAC}{14} = \frac{\sin 43^\circ}{20}$

3. Rearrange to find $\sin BAC$: $\sin BAC = \frac{14 \cdot \sin 43^\circ}{20}$

   Using a calculator: $\sin BAC = \frac{14 \cdot 0.682}{20} = 0.4774$

4. Find $BAC$: Use the inverse sine function: $BAC = \sin^{-1}(0.4774)$

   Calculating: $BAC \approx 28.6^\circ$

Final Answer:

$\angle BAC = 28.6^\circ \, (\text{to 3 significant figures})$

Let me know if you need further clarification or detailed steps!

Related Questions:

1. How is the Sine Rule applied to non-right triangles?
2. Can the Sine Rule handle ambiguous cases (two possible angles)?
3. What other methods can solve a triangle with given sides and angles?
4. How would this problem change if the angle $BCA$ were obtuse?
5. How is the Cosine Rule different from the Sine Rule?

Tip:

Always ensure your calculator is set to the correct mode (degrees/radians) for angle calculations!