Find value tan 60 geometrically.

The above given ΔABC is an Equilateral triangle with side say 2a.

CD is the median of ΔABC which implies

Now,

ΔACD is Right-angled Triangle with ∠ADC = 90°.

Also, as ΔABC is equilateral which means ∠A = ∠B = ∠C = 60°.

∴ In ΔADC,

AD = a, AC = 2a

∴ AC² = AD² +CD²(By Pythagoras Theorem)

⇒ (2a)² +(a)² +CD²

⇒ 4a² – a² =CD²

⇒ CD² = 3a²

Which gives us CD = √3a

Now as ∠CAD = 60°

Hence, we got the value of tan 60 = √3 geometrically.