Question

Find the area of each triangle.$A=50,B=30,a=1$

Short answer

The area of the triangle is$0.32squareunit$

Step-by-step solution

Step 1.  Given information    

The given data is$A=50,B=30,a=1$

Step 2. Find the length of sides of b

Using Law of Sines, $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

here. $A=50,B=30,a=1$

$$\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin 50}{1}=\frac{\sin 30}{b} \\ b=\frac{\sin 30}{\sin 50} \\ b=0.65 \end{gathered}$$

Step 3. Find the angle C

Since the angle A,B,C are the angles of a triangle,

$$\begin{gathered} A+B+C=180 \\ 50+30+C=180 \\ C=180-80 \\ C=100 \end{gathered}$$

Step 4. Find the area of the triangle,

The area of the triangle is$$\begin{gathered} k=\frac{1}{2}ab\sin C \\ k=\frac{1}{2}1\times 0.65\times \sin 100 \\ k=0.32 \end{gathered}$$