A wire of length 2 metre is cut into three pieces so as W IV . the sides of a triangle. If the two angles of the triangle be 35° and 85°, find in metre the lengths of the sides. Given sin 35º = 0.5736, sin 60° = 0.8660 and sin 85° = 0.9962.

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( a+b+c=2 . quad A=35 ) ( frac{a}{sin A}=frac{b}{sin B}=frac{c}{sin C} quad begin{array}{l}B=85 C=60end{array} ) ( Rightarrow quad frac{a}{b}=0.575 quad Rightarrow quad a=0.57 b ) ( b=|a| cdot 74 a ) ( Rightarrow quad frac{a}{c}=0.662 Rightarrow a=0.662 mathrm{c} ) ( 1.51 a ) ( therefore a+1.74 a+1.51 a=2 ) ( Rightarrow quad 4.25 a=2 ) ( a=0.47 m ) ( frac{f^{b}=0.818 m}{1 c=0.712 m} )

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