Answer:
9.2
Step-by-step explanation:
Well since you're given two angles you can find the other angle by subtracting the sum of those two known angles from 180
so m<C = 180 - (52 + 19) = 109
m<C = 109
So know that you have the angle C and the side c, as well as the angle A you can use this information to solve for side a using the law of sines.
The law of sines states that: [tex]\frac{a}{sin A} = \frac{c}{sin C}[/tex] which works for any two sides and angles of the triangle.
So now we can plug the known information in to solve for side a
[tex]\frac{a}{sin 52} = \frac{11}{sin 109}\\\\a=\frac{11}{sin109}*sin52\\a\approx11.634 * 0.788\\a\approx9.168\\a\approx9.2[/tex]
