Question

Two sides and an angle SSA of a triangle are given determine whether the given measurements produce one triangle two triangles or no triangle at all solve each triangle that results a=13 b=16.9 A=26 degrees

Answer 1

Given:

a = 13

b = 16.9

A = 26 degrees

Asked: What are the values for angles B and C and side c?

Solution:

To solve this problem, we will be needing the formula for the sine law.

Sine Law Formula:

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

Now, we will first solve for the angle B.

$\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{13}{\sin 26}=\frac{16.9}{\sin B} \\ 13\sin B=16.9\sin 26 \\ \frac{13\sin B}{13}=\frac{16.9\sin 26}{13} \\ \sin B=\frac{16.9\sin26}{13} \\ B=\sin ^{-1}(\frac{16.9\sin26}{13}) \\ B=34.75203189 \\ B=35\text{ degr}ees \end{gathered}$

Now that we have angle B, we can now find angle C by combining all the angles and equate it to 180 degrees.

$\begin{gathered} A+B+C=180 \\ 26+35+C=180 \\ 61+C=180 \\ C=180-61 \\ C=119\text{ degr}ees \end{gathered}$

In order to find side c, we will use again the sine law formula.

$\begin{gathered} \frac{a}{\sin A}=\frac{c}{\sin C} \\ \frac{13}{\sin 26}=\frac{c}{\sin 119} \\ 13\sin 119=c\sin 26 \\ \frac{13\sin119}{\sin26}=\frac{c\sin 26}{\sin 26} \\ c=\frac{13\sin119}{\sin26} \\ c=25.9370542 \end{gathered}$

ANSWER:

Angle B = 35 degrees

Angle C = 119 degrees

Side c = 25.9