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