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=√(4^2+9^2)=√(97)`

Then by the law of sines,

`(\sin A)/(BC)=(\sin C)/(AB)\iff\frac1{√(97)}=\frac{\sin C}4\implies\sin C=\frac4{√(97)}`

`\implies C=\sin^(-1)\frac4{√(97)}\approx24^\circ`