Question

Solve each triangle using either the Law of Sines or the Law of Cosines

$B=20°,C=75°,b=5$

Short answer

The required triangle is

$$\begin{gathered} A=85° \\ a=14.56 \\ c=14.12 \end{gathered}$$

Step-by-step solution

Given information

$B=20°,C=75°,b=5$

To find : Angle A and sides a ,c

Calculation

We know,

$$\begin{gathered} A+B+C=180° \\ \Rightarrow A+20°+75°=180° \\ \Rightarrow A=180°-20°-75° \\ =85° \end{gathered}$$

By Law of Sines,

$$\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \Rightarrow \frac{\sin 20}{5}=\frac{\sin 75}{c} \\ \Rightarrow c=\frac{5\sin 75}{\sin 20} \\ =14.12 \\ \frac{\sin A}{a}=\frac{\sin C}{C} \\ \Rightarrow \frac{\sin 85}{a}=\frac{\sin 75}{14.12} \\ \Rightarrow a=\frac{14.12\sin 85}{\sin 75} \\ =14.56 \end{gathered}$$