Question

Find the area of the triangle. Round answer to two decimal places.

$A=50°,C=20°,a=3$

Short answer

The area of the triangle is 1.89 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}A& =& 50°\\ C& =& 20°\\ a& =& 3\end{array}$

Step 2. Determine the third angle.

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

$\begin{array}{rcl}A+B+C& =& 180°\\ 50°+B+20°& =& 180°\\ B& =& 180°-70°\\ B& =& 110°\end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

$K=\frac{a^2\sin B\sin C}{2\sin A}$

Substitute the values in the above formula.

$\begin{array}{rcl}K& =& \frac{\left(3{)}^2\sin \right(110°\left)\sin \right(20°)}{2\sin (50°)}\\ K& =& \frac{9(0.94)(0.342)}{2(0.766)}\\ K& =& 1.88859...\\ K& \approx & 1.89\end{array}$

Step 4. Conclusion.

The area of the triangle is 1.89 square units.