Question

geometrically find the value of cot 60 degree

Answer 1

value of cot 60 is
$\frac{1}{ \sqrt{3} }$

Answer 2

Let there be an equilateral triangle ABC of side a
Draw a perpendicular with A as vertex.
The perpendicular from A will meet BC at D
BD =DC= a/2

In triangle ADB,
using Pythagoras theorem,
AD^2 +DB^2 = AB^2

AD^2 = a×a - a/2×a/2 =3a^2/4
AD = √3a/2
So, in triangle ADB is right angled with
angle ABD= 60
So, cot 60 = base/perpendicular =a/2÷√3a/2
=1/√3
HENCE PROVED