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Q. 30

Expert-verifiedFound in: Page 541

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

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

$A=70\xb0,B=60\xb0,c=4$

The area of the triangle is 8.50 square units.

The given values are:

$\begin{array}{rcl}A& =& 70\xb0\\ B& =& 60\xb0\\ c& =& 4\end{array}$

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

$\begin{array}{rcl}A+B+C& =& 180\xb0\\ 70\xb0+60\xb0+C& =& 180\xb0\\ C& =& 180\xb0-130\xb0\\ C& =& 50\xb0\end{array}$

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.

$\begin{array}{rcl}K& =& \frac{\left(4{)}^{2}\mathrm{sin}\right(70\xb0\left)\mathrm{sin}\right(60\xb0)}{2\mathrm{sin}(50\xb0)}\\ K& =& \frac{16(0.9397)(0.866)}{2(0.766)}\\ K& =& 8.499009...\\ K& \approx & 8.50\end{array}$

The area of the triangle is 8.50 square units.

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