Chapter 6.1, Problem 44E

(a)

To determine

Todraw:The triangle that represent the triangle by indicating the height of pole with the help of variable.

Explanation of Solution

Given:

A triangle is indicating the height of pole.

The triangle is shown in figure below.

  

Figure (1)

Therefore, the required diagram is shown in Figure (1).

(b)

To determine

To write:The equation involving unknown quantity.

Explanation of Solution

The law of sine is given by,

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

The value of $A$ is calculated as,

  $\begin{array}{c}A=180°-90°-20°-12°\\ =58°\end{array}$

Now by the law of sine.

  $\begin{array}{c}\frac{16}{\sin 58°}=\frac{c}{\sin 20°}\\ c=\frac{16\sin 20°}{\sin 58°}\end{array}$

Therefore, the equation involving unknown quantity is $c=\frac{16\sin 20°}{\sin 58°}$ .

(c)

To determine

To find:The height of the flagpole.

Explanation of Solution

The law of sine is given by,

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

The value of $A$ is calculated as,

  $\begin{array}{c}A=180°-90°-20°-12°\\ =58°\end{array}$

Now by the law of sine.

  $\begin{array}{c}\frac{16}{\sin 58°}=\frac{c}{\sin 20°}\\ c=\frac{16\sin 20°}{\sin 58°}\\ c=6.4\end{array}$

Therefore, the height of the pole is $6.4\text{in}$ .