Question

Determine the remaining sides and angles of the triangle ABCwhat is the measure of angle Bwhat is the length of side awhat is the length of side b

Answer 1

Angles A, B, and C together add to 180 degrees.

We can find Angle B:

$\begin{gathered} 100.4+38.1+\angle B=180 \\ 138.5+\angle B=180 \\ \angle B=41.5\degree \end{gathered}$

side a is opposite angle A, side b is opposite angle B.

We now have pairs for which we can solve for a side [either a or b].

We will use sin rule, which is:

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Let's find a first using known and unknown pairs:

$\begin{gathered} \frac{a}{\sin A}=\frac{c}{\sin C} \\ \frac{a}{\sin38.1}=\frac{48.4}{\sin 100.4} \\ a\sin 100.4=48.4\sin 38.1 \\ a=\frac{48.4\times\sin 38.1}{\sin 100.4} \\ a=30.36 \end{gathered}$

By similar process, we find b:

$\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C} \\ \frac{b}{\sin41.5}=\frac{48.4}{\sin 100.4} \\ b\sin 100.4=48.4\sin 41.5 \\ b=\frac{48.4\times\sin 41.5}{\sin 100.4} \\ b=32.61 \end{gathered}$

Angle B = 41.5 degrees

Side a = 30.36

Side b = 32.61