Question

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

$B=10°,C=100°,b=2$

Short answer

The area of the triangle is 10.66 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}B& =& 10°\\ C& =& 100°\\ b& =& 2\end{array}$

Step 2. Determine the third angle.

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

$\begin{array}{rcl}A+B+C& =& 180°\\ A+10°+100°& =& 180°\\ A& =& 180°-110°\\ A& =& 70°\end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

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

Substitute the values in the above formula.

$\begin{array}{rcl}K& =& \frac{\left(2{)}^2\sin \right(70°\left)\sin \right(100°)}{2\sin (10°)}\\ K& =& \frac{4(0.9397)(0.9848)}{2(0.1736)}\\ K& =& 10.66148...\\ K& \approx & 10.66\end{array}$

Step 4. Conclusion.

The area of the triangle is 10.66 square units.