Q. 64.0( 5 Votes )

Find value tan 60

Answer :


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.


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