Question Number 18755 by ram1234 last updated on 29/Jul/17
$$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{if}\:{c}\:=\:\mathrm{2},\:{A}\:=\:\mathrm{120}°,\:{a}\:=\:\sqrt{\mathrm{6}}\:, \\ $$$$\mathrm{then}\:\:{C}\:= \\ $$
Answered by Tinkutara last updated on 29/Jul/17
$$\frac{\mathrm{sin}\:{C}}{\mathrm{2}}\:=\:\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}{\sqrt{\mathrm{6}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$$\mathrm{sin}\:{C}\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}} \\ $$$${C}\:=\:\mathrm{45}° \\ $$