Question

if sin A=1/root2,tan(A-B)=1/root3 find b?
if tanteeta=a/b find sin teeta? please answer these 2 questions

Answer 1

$sin(A)=\frac{1}{\sqrt{2}}$ → $A=45^{o}$.
Then, $tan(A-B)=\frac{1-tanB}{1+tanB}=\frac{1}{\sqrt{3}}$.
Then, $tanB=2-\sqrt{3}$ → $B=15^{o}$.

$tanA=\frac{a}{b}$ then $sinA=\frac{a}{\sqrt{a^{2}+b^{2}}}$.