3.93: Triangle with given angles (no calculator)

0606/23/O/N/23 — Question 7 · 7 marks

Do not use a calculator in this question.

In triangle $ABC$, angle $A=60^{\circ}$, angle $B=75^{\circ}$, angle $C=45^{\circ}$ and $AB=\sqrt{2}$.
You may use $\mathrm{sin}\,60^{\circ}=\dfrac{\sqrt{3}}{2}$, $\mathrm{sin}\,45^{\circ}=\dfrac{\sqrt{2}}{2}$, $\mathrm{cos}\,60^{\circ}=\dfrac{1}{2}$, $\mathrm{cos}\,45^{\circ}=\dfrac{\sqrt{2}}{2}$, $\mathrm{tan}\,60^{\circ}=\sqrt{3}$, $\mathrm{tan}\,45^{\circ}=1$.