Question

Solve each triangle.

Short answer

The value of the angle is $A=70$

The length of the sides of the triangle$$\begin{gathered} b=3.4 \\ a=9.4 \end{gathered}$$

Step-by-step solution

Step 1. Given information   

The given data from the graph is$$\begin{gathered} B=20 \\ c=10 \end{gathered}$$

Step 2. Find the angle A

The Sum of all angles of a triangle is $180$

Therefore,$$\begin{gathered} A+20+90=180 \\ A=180-110 \\ A=70 \end{gathered}$$

Step 3. Find the length of b

By using the law of sines.$$\begin{gathered} \sin 20=\frac{b}{10} \\ b=10s\mathrm{in}20 \\ b=3.4 \end{gathered}$$

Step 4. By using law of sines

$$\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin 70}{a}=\frac{\sin 20}{b}=\frac{\sin 90}{10} \\ \frac{\sin 70}{a}=\frac{\sin 90}{10} \\ a=10\sin 70 \\ a=9.39 \end{gathered}$$