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Q. 30

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Found in: Page 541

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the area of the triangle. Round answer to two decimal places.$A=70°,B=60°,c=4$

The area of the triangle is 8.50 square units.

See the 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:

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

Substitute the values in the above formula.

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

## Step 4. Conclusion.

The area of the triangle is 8.50 square units.