Question

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

$A=40°,B=20°,a=2$

Short answer

The area of the triangle is 0.92 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}A& =& 40°\\ B& =& 20°\\ a& =& 2\end{array}$

Step 2. Determine the third angle.

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

$\begin{array}{rcl}A+B+C& =& 180°\\ 40°+20°+C& =& 180°\\ C& =& 180°-60°\\ C& =& 120°\end{array}$

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.

$\begin{array}{rcl}K& =& \frac{\left(2{)}^2\sin \right(20°\left)\sin \right(120°)}{2\sin (40°)}\\ K& =& \frac{4(0.342)(0.866)}{2(0.643)}\\ K& =& 0.921219...\\ K& \approx & 0.92\end{array}$

Step 4. Conclusion.

The area of the triangle is 0.92 square units.