# How do you evaluate #tan^-1(sqrt3/3)# without a calculator?

##### 1 Answer

Sep 29, 2016

#### Explanation:

Consider a triangle with sides in ratio

This is a right angled triangle since:

#1^2+sqrt(3)^2 = 1+3 = 4 = 2^2#

In fact, it is one half of an equilateral triangle, hence has angles

Now

Hence we find:

#tan (pi/6) = 1/sqrt(3) = sqrt(3)/3#

Since