The value of sin of $30$ degrees can be derived in theoretical approach but it requires knowledge on properties of right triangle when its angle is equal to $30^°$. You can even find the value of sin of angle $30$ degrees geometrically by constructing a right triangle with $30$ degrees angle with the help of geometric tools.

- From point $\small G$, draw a straight line on a plane horizontally.
- Draw a $30$ degrees line from point $\small G$ by using protractor and ruler.
- Set compass to any length. It is set to $7 \, cm$ in this case by considering measurement of ruler. Later, draw an arc on $30$ degrees line from point $\small G$ and it intersects the $30$ degrees line at point $\small H$.
- Finally, draw a perpendicular line to horizontal line from point $\small H$ and it intersects the horizontal line perpendicularly at point $\small I$. This procedure constructs a right triangle (called $\small \Delta IGH$) geometrically.

In $\Delta IGH$, the length of hypotenuse is $GH = 7 \, cm$ and the angle of right triangle is $30$ degrees. So, write sin of angle $30$ degrees in the form of ratio of lengths of the sides.

$\sin{(30^°)} \,=\, \dfrac{HI}{GH}$

The length of opposite side is required to calculate the exact value of sin $30$ degrees. So, take a ruler and measure the length of the opposite side. You will measure that the length of opposite side is $3.5 \, cm$ exactly.

$\implies \sin{(30^°)} \,=\, \dfrac{3.5}{7}$

$\implies \require{cancel} \sin{(30^°)} \,=\, \dfrac{\cancel{3.5}}{\cancel{7}}$

$\implies \sin{(30^°)} \,=\, \dfrac{1}{2}$

It is exact value of sin of $30$ degrees in fraction and its value in decimal is given below.

$\,\,\, \therefore \,\,\,\,\,\, \sin{(30^°)} \,=\, 0.5$

In this way, the value of sine of angle $30$ degrees can be derived experimentally in trigonometry by using geometric tools.

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.