Solve : In a triangle ABC , $\tan A =2$ and $\tan B = 3/2$ . If $c = \sqrt{65}$ then the circumradius of the triangle is?

Question

Let me be truthful to you, I can't figure out what is the first step to proceed. Can you help me in this ? But I have tried by this formula :

$$ \cot B = \frac{a^2 + c^2 - b^2}{4\Delta} $$ and thought to use

$$\Delta = \frac{abc}{4R}$$

but failed

Answer 1

Hint: Use the formula $$\sin(C)=\frac{c}{2R}$$ and the angle $C$ can be found by the equation

$$C=\pi-\arctan(2)-\arctan(\frac{3}{2})$$ and $$c=\sqrt{65}$$ Can you proceed? For your Control: $$R=\frac{65}{14}$$