Question

Find the value of tan 60°, geometrically.

Answer 1

In ∆ABC, let AD ⊥ BC
Consider an equilateral triangle ABC with each side 2a.
AD is the bisector of BC and gives BD = CD = a
In ∆ABD, ∠D is right angle, hypotenuse AB = 2a

So, by pythagoras theorem, we have AB²=AD²+BD²