Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If $b=3c$ and $C-B={90}^{\circ }$ , then find the value of $\tan B$

• A. $3$
• B. $\frac{1}{3}$
• C. $2\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is A $3$

Given $b=3c,C-B={90}^{\circ }$

$\Rightarrow \frac{b}{c}=3,C={90}^{\circ }+B$

Using sine rule,

$\frac{b}{\sin B}=\frac{c}{\sin C},$

$\Rightarrow \frac{\sin B}{\sin C}=\frac{b}{c}=\frac{\sin B}{\sin ({90}^{\circ }+B)}$

$=>\tan B=3$