Question

Solve the triangle using the Law of Sines. (Assume c = 55, _A = 549, and zB = 20°. Round lengths to two decimal places.) I just want a....and b

Answer 1

Saw of Lines:

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

Side c is given as

c = 55

Also,

b = 20°

Now, we can use the law and solve. Shown below:

$\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C} \\ \frac{b}{\sin20}=\frac{55}{\sin 106} \\ b\sin 106=55\sin 20 \\ b=\frac{55\sin 20}{\sin 106} \\ b=19.57 \end{gathered}$

Then, we want to solve for a. Shown below:

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

So, substituting, we have:

$\begin{gathered} \frac{a}{\sin 54}=\frac{55}{\sin 106} \\ a\sin 106=55\sin 54 \\ a=\frac{55\sin 54}{\sin 106} \\ a=46.29 \end{gathered}$