Question

In the adjoining figure of traingle ABC , angle BCA= 120 and AB= c,BC=a, AC=b then what is the relation of a, b,c

Answer 1

Answer:

In △CDB,

BC2 =  CD2 + BD2      [By Pythagoras Theorem]

BC2 =  CD2 + (DA+AB)2  

BC2 =  CD2 + DA2 + AB2 + (2×DA×AB)         (i)

In △ADC,

CD2 + DA2 = AC2      (ii)  [By Pythagoras Theorem]

Also, Cos60∘ = AD/AC

AC = 2AD       (iii)

Putting the values from (ii) and (iii) in (i), we get

BC2 =  AC2 + AB2 + (AC×AB)

a2 = b2 +  c2 + bc