Question

Solve each triangle.

$a=3,b=3,c=2$

Short answer

The required triangle is

$$\begin{gathered} A=70.73° \\ B=70.73° \\ C=38.54° \end{gathered}$$

Step-by-step solution

Given information

$a=3,b=3,c=2$

To find the angles A,B,C

Calculation

$$\begin{gathered} ForA: \\ \cos \left(A\right)=\frac{b^2+c^2-a^2}{2bc} \\ =\frac{3^2+2^2-3^2}{2\times 3\times 2} \\ =0.33 \\ A={\cos }^{-1}\left(0.33\right) \\ =70.73° \\ ForB: \\ \cos \left(B\right)=\frac{a^2+c^2-b^2}{2ac} \\ =\frac{3^2+2^2-3^2}{2\times 3\times 2} \\ =0.33 \\ B={\cos }^{-1}\left(0.33\right) \\ =70.73° \end{gathered}$$

Since we know A and B

$$\begin{gathered} C=180°-A-B \\ =180°-70.73-70.73 \\ =38.54° \end{gathered}$$