Answer:
[tex]a=10.92 units[/tex]
[tex]b=14.51 units[/tex]
Step-by-step explanation:
We are given that c=6 units
[tex]\angle A=43^{\circ}[/tex]
[tex]\angle B=115^{\circ}[/tex]
We have to find the side length a and b.
We know that sum of angles of a triangle =180 degrees
[tex]\angle A+\angle B+\angle C=180[/tex]
Substitute the values then we get
[tex]43+115+\angle C=180[/tex]
[tex]158+\angle C=180[/tex]
[tex]\angle C=180-158=22^{\circ}[/tex]
sine law: [tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 43^{\circ}}=\frac{6}{sin 22^{\circ}}[/tex]
[tex]a=\frac{6}{sin 22^{\circ}}\times sin 43^{\circ}[/tex]
[tex]a=10.92 units[/tex]
[tex]\frac{b}{sin 115^{\circ}}=\frac{6}{sin 22^{\circ}}[/tex]
[tex] b=\frac{6}{sin 22^{\circ}}\times sin 115^{\circ}=14.51[/tex]
[tex]b=14.51 units[/tex]
