Construct a triangle with b, c and $|\angle B - \angle C|$ How can we construct a triangle with given b, c and $|\angle B - \angle C|$?


Let $B-C=x$ we know $B+C=180-A$ so we get a relation between B and A its $B=90-A/2+x/2$ so $C=90-A/2-x/2$ so now you said you know the value of $x$ ie $B-C$ so you know $A+B+C=180$ now you have all three angles in terms of A so get it. Then find the remaining side if you want use Sine rule ie $\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$ get a ie side opposite to angle A and you can construct a triangle.
