Chapter 8, Problem 44RE

To determine

To find: The area of the triangle.

Answer to Problem 44RE

The value of the area of the triangle is $0.93\text{square}\text{unit}$ .

Explanation of Solution

Given:

The given sidesand angles are,

  $\begin{array}{l}A=10°\\ C=40°\\ a=3\end{array}$

Calculation:

Consider the given sides and angle are,

  $\begin{array}{l}A=10°\\ C=40°\\ a=3\end{array}$

Consider the sum angle property is,

  $A+B+C=180°$

Then,

  $\begin{array}{l}10°+40°+B=180°\\ B=130°\end{array}$

Consider the law of Sine is,

  $\frac{\sin A}{a}=\frac{\sin C}{c}$

Then,

  $\begin{array}{l}\frac{\sin 10°}{a}=\frac{\sin 40°}{3}\\ a=3\frac{\sin 10°}{\sin 40°}\\ a=0.81\end{array}$

Consider the formula for the area of the triangle is,

  $K=\frac{1}{2}ac\sin B$

Then,

  $\begin{array}{c}K=\frac{1}{2}\left(0.81\right)\left(3\right)\sin \left(130°\right)\\ =0.93\text{square}\text{unit}\end{array}$