# Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 722: 56

The height of the wall is $\text{15}\text{.6 feet}$.

#### Work Step by Step

By observing the figure, we will find A. We will use the linear pair of angles to get, \begin{align} & A=90{}^\circ -6{}^\circ \\ & =84{}^\circ \end{align} Now, to find angle C we will use the angle sum property of triangles: \begin{align} & A+B+C=180{}^\circ \\ & 84{}^\circ +22{}^\circ +C=180{}^\circ \\ & C=180{}^\circ -106{}^\circ \\ & C=74{}^\circ \end{align} Using the law of sines we will find a: \begin{align} & \frac{a}{\sin A}=\frac{c}{\sin C} \\ & \frac{a}{\sin 22{}^\circ }=\frac{40}{\sin 74{}^\circ } \\ & c=\frac{40\sin 22{}^\circ }{\sin 74{}^\circ } \\ & \approx 15.6 \end{align} Therefore, the height of the wall is $\text{15}\text{.6 feet}$.

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