Here is Mario's answer to a question - OCR - GCSE Maths - Question 3 - 2018 - Paper 4

To find the length $x$, we can use the sine rule since we have a non-right-angled triangle.

The sine rule states that:

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

In our triangle:

• Let $a = 6$ mm (opposite angle $88^{\circ}$)
• Let $b = x$ mm (opposite angle $43^{\circ}$)
• Therefore: $\frac{6}{\sin(88^{\circ})} = \frac{x}{\sin(43^{\circ})}$

Rearranging gives: $x = \frac{6 \cdot \sin(43^{\circ})}{\sin(88^{\circ})}$

Calculating this value:

• $\sin(88^{\circ}) \approx 0.998$ and $\sin(43^{\circ}) \approx 0.682$.
• Thus: $x \approx \frac{6 \cdot 0.682}{0.998} \approx 4.1 \text{ mm (2 d.p.)}$