Chapter 4.3, Problem 26E

To determine

The missing values by construction of an appropriate triangle.

Answer to Problem 26E

Table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${60}^0$	$\frac{\pi }{3}$	1.73

Explanation of Solution

Given info:

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan		$\frac{\pi }{3}$

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 degrees

  $\begin{array}{l}\text{Angle in degree = Angle in radian }\times \frac{180}{\pi }\\ \text{Angle in degree = }\frac{\pi }{3}\times \frac{180}{\pi }\\ \text{Angle in degree = }60\end{array}$

Now for calculating $\tan {60}^0$ , let us construct a right-angled triangle with ${60}^0$

  

We have from the given drawing

  $\tan 60=\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{5.20}{3}=\text{1}\text{.73}$

So, table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${60}^0$	$\frac{\pi }{3}$	1.73

Conclusion:

Thus,the table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
tan	${60}^0$	$\frac{\pi }{3}$	1.73