(a) Finding \( BC \) using the Cosine Rule:

\[ BC^2 = 15^2 + 25^2 – 2 \cdot 15 \cdot 25 \cdot \cos(22^\circ) \]

\[ BC = \sqrt{15^2 + 25^2 – 2 \cdot 15 \cdot 25 \cdot \cos(22^\circ)} \]

\[ BC = 12.4 \text{ cm} \, (12.4343\ldots) \]

(b) Finding \( \angle ABC \) using the Sine Rule or Cosine Rule:

Using the Sine Rule:

\[ \frac{12.4343\ldots}{\sin(22^\circ)} = \frac{15}{\sin(\angle ABC)} \]

Or using the Cosine Rule:

\[ \cos(\angle ABC) = \frac{25^2 + 12.4343\ldots^2 – 15^2}{2 \cdot 25 \cdot 12.4343\ldots} \]

Solving gives:

\[ \angle ABC = 26.9^\circ \, (26.8658\ldots^\circ) \]

…………………………..Markscheme…………………………..

(a)

• Correct calculation of \( BC = 12.4 \) cm (or \( 12.4343… \)).

(b)

• Correct calculation of \( \angle ABC = 26.9^\circ \) (or \( 26.8658…^\circ \)).