Question

Abc is a triangle, ac=19cm bc=17cm and angle bac=60 degrees. calculate the size of angle abc? answer

Answer 1

$\frac{|AC|}{sin\angle ABC}=\frac{|BC|}{sin\angle BAC}\\\\|AC|=19cm;\ |BC|=17cm;\ |\angle BAC|=60^o;\ |\angle ABC|=x\\\\\frac{19}{sinx}=\frac{17}{sin60^o}\\\\cross\ multiply\\\\17sinx=19sin60^O\\\\17sinx=19\cdot\frac{\sqrt3}{3}\ \ \ \ /:17\\\\sinx=\frac{19\sqrt3}{51}\\\\sinx\approx0.6453\Rightarrow x\approx40^o11'\\\\Answer:|\angle ABC|\approx40^o11'$