You have learned how to derive the value of cos 18 degrees in trigonometric method. It is time to learn how to derive the value of cosine of angle eighteen degree experimentally in geometric method. It is practically possible by constructing a right triangle (or right angled triangle) with an angle of eighteen degrees.

- Use a ruler and draw a line of any length horizontally. For example, $10 \, cm$ line is drawn and it is called the line $\overline{DE}$.
- Use a protractor and draw a perpendicular line to the line segment $\overline{DE}$ at point $E$.
- Now, coincide the middle point of the protractor with the point $D$, then mark on plane at $18$ degrees indication line of protractor in anticlockwise direction. Finally, draw a line from point $D$ through $18$ degrees mark and it intersects the perpendicular line at point $F$.

The three steps helped us in constructing a right triangle, known as $\Delta FDE$. In this case, the angle of the right angled triangle is $18$ degrees. So, let us evaluate the cosine of angle $\dfrac{\pi}{10}$ radian.

$\cos{(18^\circ)} \,=\, \dfrac{DE}{DF}$

The length of the adjacent side ($\overline{DE}$) is $10 \, cm$ but the length of the hypotenuse ($\overline{DF}$) is unknown. However, it can be measured by using a ruler and it is measured that the length of the hypotenuse is $10.5 \, cm$.

$\implies$ $\cos{(18^\circ)} \,=\, \dfrac{10}{10.5}$

$\implies$ $\cos{(18^\circ)} \,=\, 0.9523809523\ldots$

Latest Math Topics

Nov 03, 2022

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved