Question

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

$A=70°,B=60°,c=4$

Short answer

The area of the triangle is 8.50 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}A& =& 70°\\ B& =& 60°\\ c& =& 4\end{array}$

Step 2. Determine the third angle.

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

$\begin{array}{rcl}A+B+C& =& 180°\\ 70°+60°+C& =& 180°\\ C& =& 180°-130°\\ C& =& 50°\end{array}$

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.

$\begin{array}{rcl}K& =& \frac{\left(4{)}^2\sin \right(70°\left)\sin \right(60°)}{2\sin (50°)}\\ K& =& \frac{16(0.9397)(0.866)}{2(0.766)}\\ K& =& 8.499009...\\ K& \approx & 8.50\end{array}$

Step 4. Conclusion.

The area of the triangle is 8.50 square units.