Answer:
The correct answer option is A) A=126.2°, B=19.2°, and C=34.6°.
Step-by-step explanation:
Using cosine rule to find angle A:
[tex]a^2=b^2+c^2-2bc cos A[/tex]
Substituting the given values in the formula to get:
[tex]27^2=11^2+19^2-2(11)(19) cos A[/tex]
[tex]729-482=-418cos A[/tex]
[tex]A=cos'(-0.590)[/tex]
A = 126.2°
Now that we have found one angle, we can use sine rule to find the other two angles.
[tex]\frac{SinA}{a} =\frac{Sin B}{b}[/tex]
[tex]\frac{Sin 126.2}{27} =\frac{Sin B}{11}[/tex]
[tex]B=sin'(0.328)[/tex]
B = 19.2°
[tex]\frac{SinB}{b} =\frac{Sin C}{c}[/tex]
[tex]\frac{Sin 19.2}{11} =\frac{Sin C}{19}[/tex]
[tex]C=sin'(0.567)[/tex]
C = 34.6°
Therefore, the correct answer option is A) A=126.2°, B=19.2°, and C=34.6°.
