Question

Solve the triangle if possible: a = sqrt(2) c=2sqrt(2)
B = 33 degrees.

Answer 1

First, use the law of cosines to solve for the 3rd side. The law of cosines says:

\[b^2=a^2+c^2-2ac\cos\theta\]

In this case:

\[b^2=2+8-8\cos(33^\circ) = 3.29\]
\[b=1.81\]

From there, use the law of sines to solve for the other angles. For example:

\[\frac{a}{\sin A}=\frac{b}{\sin B}\]
\[\sin A=\frac{a\sin B}{b} = 0.42\]
\[A = 25.1^\circ\]
You can use the same method to find angle C.

Answer 2

Thank you @srossd