Chapter 4.3, Problem 23E

To determine

The missing values by construction of an appropriate triangle.

Answer to Problem 23E

Table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${30}^0$	$\frac{\pi }{6}$	0.577

Explanation of Solution

Given info:

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${30}^0$

Formula used:

  $\begin{array}{l}\text{Angle in radian = Angle in degree }\times \frac{\pi }{180}\\ \text{Angle in degree = Angle in radian}\times \frac{180}{\pi }\end{array}$

Calculation:

First let us find angle in radians

  $\begin{array}{l}\text{Angle in radian = Angle in degree }\times \frac{\pi }{180}\\ \text{Angle in radian = }30\times \frac{\pi }{180}\\ \text{Angle in radian =}\frac{\pi }{6}\end{array}$

Now for calculating $\tan {30}^0$ , let us construct a right-angled triangle with ${30}^0$

  

We have from the given drawing

  $\tan 30=\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{2.31}{4}=\text{0}\text{.577}$

So, table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${30}^0$	$\frac{\pi }{6}$	0.577

Conclusion:

Thus,the table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${30}^0$	$\frac{\pi }{6}$	0.577