Chapter 14, Problem 5CLR

To determine

To find: The area of the triangle $\Delta ABC$ .

Answer to Problem 5CLR

The area of the triangle $\Delta ABC$ is $14.1$ square unit.

Explanation of Solution

Given:

The given values are $a=5$ , $b=9$ , and $c=6$ .

Calculation:

Use the cosine formulas to find the angles.

Substitute $a=5$ , $b=9$ , and $c=6$ in the formula $s=\frac{1}{2}\left(a+b+c\right)$ to find $s$ .

  $\begin{array}{c}s=\frac{1}{2}\left(5+9+6\right)\\ =\frac{20}{2}\\ =10\end{array}$

Substitute $a=5$ , $b=9$ , $c=6$ and $s=10$ in the formula $A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ to find the area.

  $\begin{array}{c}A=\sqrt{10\left(10-5\right)\left(10-9\right)\left(10-6\right)}\\ =\sqrt{200}\\ =14.1\end{array}$

Therefore, the area of the triangle $\Delta ABC$ is $14.1$ square unit.