Chapter 8.6, Problem 1ACYP

To determine

To Find: The $x$ rounded to the nearest tenth in the figure below.

  

Answer to Problem 1ACYP

The value of $x$ is approx. $7.08$ .

Explanation of Solution

We see two angles and a non-included side (AAS) therefore we use law of Sines to find the value of $x$ .

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

By the properties: $\frac{\sin {78}^{\circ }}{8}=\frac{\sin {60}^{\circ }}{x}$

Applying Cross Products Property:

  $\begin{array}{c}x\cdot \sin {78}^{\circ }=8\cdot \sin {60}^{\circ }\\ x=\frac{8\cdot \sin {60}^{\circ }}{\sin {78}^{\circ }}\end{array}$

Therefore $x$ is approximately equal to $7.08$ .

Hence, the value of $x$ is approx. $7.08$ .