Question

Solve the following non-right triangles. a. A= 37°, C= 75° , a= 11

Answer 1

To solve the given triangle:

1. Find the missing angle (angle B)

The sum of internal angles of a triangle is always 180°:

$\begin{gathered} A+B+C=180 \\ B=180-A-C \\ \\ B=180-37-75 \\ B=68 \end{gathered}$

2. Use sine law to find the b and c:

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

Find b:

$\begin{gathered} \frac{b}{\sin B}=\frac{a}{\sin A} \\ \\ b=\frac{a\cdot\sin B}{\sin A} \\ \\ b=\frac{11\cdot\sin68}{\sin37}=16.94 \end{gathered}$

Find c:

$\begin{gathered} \frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a\cdot\sin C}{\sin A} \\ \\ c=\frac{11\sin 75}{\sin 37}=17.65 \end{gathered}$