Question

With the usual notation, in $\Delta ABC$, if $\angle A+\angle B={120}^o,a=\sqrt{3}+1$ and $b=\sqrt{3}-1$ then the ratio $\angle A:\angle B$, is:

• A. $7:1$
• B. $5:3$
• C. $9:7$
• D. $3:1$

Answer 1

Answer: (A)

$7:1$

$A+B={120}^o$

$\tan \frac{A-B}{2}=\frac{a-b}{a+b}\cot \left(\frac{C}{2}\right)$

$=\frac{\sqrt{3}+1-\sqrt{3}+1}{2\left(\sqrt{3}\right)}\cot \left({30}^o\right)=\frac{1}{\sqrt{3}}\cdot \sqrt{3}=1$

$\frac{A-B}{2}={45}^o$

$\Rightarrow A-B={90}^o$
$A+B={120}^o$
_______________
$2A={210}^o$
$A={105}^o$
$B={15}^o$

$\angle A:\angle B$ = $7:1$