Question

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

$A=110°,C=30°,c=3$

Short answer

The area of the triangle is 5.44 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}A& =& 110°\\ C& =& 30°\\ c& =& 3\end{array}$

Step 2. Determine the third angle.

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

$\begin{array}{rcl}A+B+C& =& 180°\\ 110°+B+30°& =& 180°\\ B& =& 180°-140°\\ B& =& 40°\end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

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

Substitute the values in the above formula.

$\begin{array}{rcl}K& =& \frac{\left(3{)}^2\sin \right(110°\left)\sin \right(40°)}{2\sin (30°)}\\ K& =& \frac{9(0.9397)(0.6429)}{2(0.5)}\\ K& =& 5.4371...\\ K& \approx & 5.44\end{array}$

Step 4. Conclusion.

The area of the triangle is 5.44 square units.