Chapter 11.2, Problem 22WE

To determine

To Find: The area to the nearest tenth using the trigonometric table or calculator.

Answer to Problem 22WE

  $A\approx 34.2sq.unit$

Explanation of Solution

Given:

  

  

Using trigonometric ratios

  $\begin{array}{l}\cos {54}^{°}=\frac{BC}{AC}\\ \cos {54}^{°}=\frac{BC}{12}\\ (12)(0.5878)=BC\\ BC=7.0536\end{array}$

Now

  $\begin{array}{l}\tan {54}^{°}=\frac{AB}{BC}\\ \tan {54}^{°}=\frac{AB}{7.0536}\\ (1.3764)(7.0536)=BC\\ AB=9.708\end{array}$

Area of triangle

  $\begin{array}{l}A=\frac{1}{2}bh\\ Base=7.053\\ Height=9.708\\ A=\frac{1}{2}(7.053)(9.708)\\ A=34.335\\ A\approx 34.2sq.unit\end{array}$

Hence, $A\approx 34.2sq.unit$