Question

Im stuck on this one

Answer 1

ABC is a right triangle, so by Pythagoras' theorem,

$AB^2+AC^2=BC^2\implies BC=\sqrt{4^2+9^2}=\sqrt{97}$

Then by the law of sines,

$\dfrac{\sin A}{BC}=\dfrac{\sin C}{AB}\iff\dfrac1{\sqrt{97}}=\dfrac{\sin C}4\implies\sin C=\dfrac4{\sqrt{97}}$

$\implies C=\sin^{-1}\dfrac4{\sqrt{97}}\approx24^\circ$