Chapter 12, Problem 19CR

To determine

Find x.

Answer to Problem 19CR

D

Explanation of Solution

Formula Used:

Law of Cosine :

  $a^2=b^2+c^2-2bc\cos A$

Law of Sine:

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

  

Calculation:

Represent the situation and solve :

  

Use Law of Sine:

  $\begin{array}{l}\frac{8}{\sin 30°}=\frac{y}{\sin 100°}\\ \Rightarrow y=\sin 100°\cdot \frac{8}{\sin 30°}\mathrm{...............}[\text{multiply each side by sin100}°]\\ \Rightarrow y=15.76\end{array}$

Now, Use Law of Cosine to find x:

  $\begin{array}{l}\Rightarrow x^2=9^2+{15.76}^2-2(9)(15.76)\cos 110°\\ \Rightarrow x\approx 20.65\end{array}$

So, the correct option is D.