Bothaiyanaar formula for right angled (30 , 60 , 90) triangle
Pythagoras was a famous Greek philosopher and great mathematician in 495BC. Pythagoras discovered a theorem in geometry called ”Pythagoras Theorem”. In his theorem he established the relationship between the hypotenuse and the other two sides adjacent to the right angle. According to this theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides.
It can be calculated in another way without considering squares. This was actually from a Tamil poet – Bothaiyanaar – and this is useful for calculating the hypotenuse of a right angled triangle.
The approximation is good for the triangle.
![[math]\Delta[/math] ACD [math]\Longrightarrow[/math] cos[math]30^{\circ}[/math] = [math]\frac{AD}{a}[/math] [math]\Longrightarrow[/math] AD = [math]a\cdot[/math]cos[math]30^\circ[/math]
[math]\Delta[/math] BCD [math]\Longrightarrow[/math] sin[math]30^\circ[/math] = [math]\frac{BD}{b}[/math] [math]\Longrightarrow[/math] BD = [math]b\cdot[/math] sin[math]30^\circ[/math]
AC = AD + BD [math]\Longrightarrow[/math] [math]c[/math] = [math]a\cdot[/math]cos[math]30^\circ[/math] + [math]b\cdot[/math]sin[math]30^\circ[/math] [math]\approx a\cdot\frac{7}{8}+b\cdot\frac{1}{2}=a-\frac{a}{8}+\frac{b}{2}[/math] [math]\because[/math] cos[math]30^\circ\approx\frac{7}{8}[/math] & sin[math]30^\circ=\frac{1}{2}[/math]](https://www.geogebra.org/resource/hgb7dgyc/4avj7KijqCD2TCSq/material-hgb7dgyc.png)