Question

Solve each triangle.

$a=4,b=3,c=6$

Short answer

The required triangle is

$$\begin{gathered} A=35.90° \\ B=27.13° \\ C=116.97° \end{gathered}$$

Step-by-step solution

Given information

$a=4,b=3,c=6$

To find A, B, C

Calculation

$$\begin{gathered} ForA: \\ \cos \left(A\right)=\frac{b^2+c^2-a^2}{2bc} \\ =\frac{3^2+6^2-4^2}{2\times 3\times 6} \\ =0.81 \\ A={\cos }^{-1}\left(0.81\right) \\ =35.90° \end{gathered}$$

$$\begin{gathered} ForB: \\ \cos \left(B\right)=\frac{a^2+c^2-b^2}{2ac} \\ =\frac{4^2+6^2-3^2}{2\times 4\times 6} \\ =0.89 \\ B={\cos }^{-1}\left(0.89\right) \\ =27.13° \end{gathered}$$

Since we know A nd B

$$\begin{gathered} C=180°-A-B \\ =180°-35.90°-27.13° \\ =116.97° \end{gathered}$$