If the ratio in the angles of triangles are 1 : 2 :3 then find the ratio in the corresponding sides

If the ratio in the angles of triangles are 1 : 2 :3 then find the rat

1.	If the ratio in the angles of triangles are 1 : 2 :3 then find the ratio in the corresponding sides
Answer» {tex}Let\\; the \\quad angles\\ be\\quad x,2x\\; and\\; 3x\\quad then,x+2x+3x={ 180^{ o } }\\Rightarrow 6x=180\\Rightarrow x{ { =\\frac { 180 }{ 6 } } }={ 30^{ o\\\\ } }\\\\ Using\\; sine\\quad rule\\quad we\\quad have\\frac { a }{ sinA } =\\frac { b }{ sinB } =\\frac { c }{ sinC } =k(say)\\\\ Herea=k\\sin 30,b=k\\sin 60,c=k\\sin 90\\\\ \\Rightarrow a=\\frac { { { k } } }{ 2 } ,b={ { \\frac { \\sqrt { 3 } }{ 2 } } }.k,c={ 1 }.k\\\\ a{ { :b{ { : } }c } }=\\frac { { { k } } }{ 2 } { { :\\frac { k\\sqrt { 3 } }{ 2 } { { : } } } }{ 1 }.k\\\\ \\Rightarrow a{ { :b{ { : } }c } }=1{ { :\\sqrt { 3 } { { : } }2 } }{/tex}