Question

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

$B=70°,C=10°,b=5$

Short answer

The area of the triangle is 2.27 square units.

Step-by-step solution

Step 1. Given information.

The given values are:

$\begin{array}{rcl}B& =& 70°\\ C& =& 10°\\ b& =& 5\end{array}$

Step 2. Determine the third angle.

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

$\begin{array}{rcl}A+B+C& =& 180°\\ A+70°+10°& =& 180°\\ B& =& 180°-80°\\ B& =& 100°\end{array}$

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.

$\begin{array}{rcl}K& =& \frac{\left(5{)}^2\sin \right(100°\left)\sin \right(10°)}{2\sin (70°)}\\ K& =& \frac{25(0.9848)(0.1736)}{2(0.9397)}\\ K& =& 2.2741...\\ K& \approx & 2.27\end{array}$

Step 4. Conclusion.

The area of the triangle is 2.27 square units.