Solve the following triangles using the Sine Rule and angle sum property of a triangle. Round answers to the nearest whole number.

Using the angle sum property:

$$A = 180^\circ - B - C$$ $$A = 180^\circ - 44^\circ - 76^\circ$$ $$A = 180^\circ - 120^\circ$$ $$A = 60^\circ$$

Using the Sine Rule:

$$\frac{b}{\sin B} = \frac{a}{\sin A}$$ $$b = \frac{a \sin B}{\sin A}$$ $$b = \frac{24.5 \sin 44^\circ}{\sin 60^\circ}$$ $$b \approx \frac{24.5 \times 0.6947}{0.8660}$$ $$b \approx 19.65 \text{ cm}$$

Rounding to the nearest whole number:

$$b \approx \boxed{20 \text{ cm}}$$

Using the Sine Rule:

$$\frac{c}{\sin C} = \frac{a}{\sin A}$$ $$c = \frac{a \sin C}{\sin A}$$ $$c = \frac{24.5 \sin 76^\circ}{\sin 60^\circ}$$ $$c \approx \frac{24.5 \times 0.9703}{0.8660}$$ $$c \approx 27.45 \text{ cm}$$

Rounding to the nearest whole number:

$$c \approx \boxed{27 \text{ cm}}$$

2) Given: $A = 62^\circ$, $b = 14 \text{ m}$, $C = 70.75^\circ$

Using the angle sum property:

$$B = 180^\circ - A - C$$ $$B = 180^\circ - 62^\circ - 70.75^\circ$$ $$B = 180^\circ - 132.75^\circ$$ $$B = 47.25^\circ$$

Rounding to the nearest whole number:

$$B \approx \boxed{47^\circ}$$

Using the Sine Rule:

$$\frac{a}{\sin A} = \frac{b}{\sin B}$$ $$a = \frac{b \sin A}{\sin B}$$ $$a = \frac{14 \sin 62^\circ}{\sin 47.25^\circ}$$ $$a \approx \frac{14 \times 0.8829}{0.7342}$$ $$a \approx 16.84 \text{ m}$$

Rounding to the nearest whole number:

$$a \approx \boxed{17 \text{ m}}$$

Using the Sine Rule:

$$\frac{c}{\sin C} = \frac{b}{\sin B}$$ $$c = \frac{b \sin C}{\sin B}$$ $$c = \frac{14 \sin 70.75^\circ}{\sin 47.25^\circ}$$ $$c \approx \frac{14 \times 0.9442}{0.7342}$$ $$c \approx 18.00 \text{ m}$$

Rounding to the nearest whole number:

$$c \approx \boxed{18 \text{ m}}$$

3) Given: $A = 31^\circ$, $B = 65^\circ$, $c = 16 \text{ m}$

Using the angle sum property:

$$C = 180^\circ - A - B$$ $$C = 180^\circ - 31^\circ - 65^\circ$$ $$C = 180^\circ - 96^\circ$$ $$C = 84^\circ$$

Using the Sine Rule:

$$\frac{a}{\sin A} = \frac{c}{\sin C}$$ $$a = \frac{c \sin A}{\sin C}$$ $$a = \frac{16 \sin 31^\circ}{\sin 84^\circ}$$ $$a \approx \frac{16 \times 0.5150}{0.9945}$$ $$a \approx 8.29 \text{ m}$$

Rounding to the nearest whole number