Answer
B = $101.1^{o}$
a = 1.35
b = 3.23
Work Step by Step
Note: The Law of Sines is: $\frac{a}{sin(A)}$ = $\frac{b}{sin(B)}$ = $\frac{c}{sin(C)}$
To solve the triangle, we need to find a, B, and b.
Finding B:
Since we are given 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 24.3 - 54.6 = 101.1
Therefore, B = $101.1^{o}$
Finding a:
We can use the Law of Sines.
$\frac{a}{sin(24.3^{o})} = \frac{2.68}{sin(54.6^{o})}$
Therefore, a = 1.35
Finding b:
We can use the Law of Sines.
$\frac{b}{sin(101.1^{o})} = \frac{2.68}{sin(54.6^{o})}$
Therefore, b = 3.23
In total:
B = $101.1^{o}$
a = 1.35
b = 3.23
