Chapter 8, Problem 59RE

To determine

To find:The cost of the parcel.

Explanation of Solution

Consider the figure shown below.

  

Figure (1)

The value of $AC$ is calculated as,

  $\begin{array}{c}AC=\sqrt{D{C}^2+A{D}^2-2\left(AD\right)\left(DC\right)\cos 40°}\\ =\sqrt{{50}^2+{100}^2-2\left(50\right)\left(100\right)0.766}\\ =69.57\text{ft}\end{array}$

The value of $A$ is calculated as,

  $\begin{array}{c}\frac{\sin A}{a}=\frac{\sin B}{b}\\ A={\sin }^{-1}\left(\frac{20}{69.57}\sin 100°\right)\\ =16.44°\end{array}$

The value of angle $C$ is calculated as,

  $\begin{array}{c}C=180°-100°-16.44°\\ =63.66°\end{array}$

The total area is calculated as,

  $\begin{array}{c}A=\left(\frac{1}{2}\left(50\right)100\sin 40°\right)+\left(\frac{1}{2}\left(20\right)69.57\sin 63.66°\right)\\ =1606.96+623.47\\ =2230.43{\text{ft}}^2\end{array}$

The cost of parcel is calculated as,

  $\begin{array}{c}\text{COST}=100\times A\\ =100\times 2230.43\\ =\$223043\end{array}$

Therefore, the cost of the parcel is $\$223043$ .