Question

If the angles of a triangle be in the ratio 1 : 2 : 7, then the ratio of its greatest side to the least side is

• A. 1:2
• B. 2:1
• C. $(\sqrt{5}+1):(\sqrt{5}-1)$
• D. $(\sqrt{5}-1):(\sqrt{5}+1)$

Answer 1

The correct option is C

$(\sqrt{5}+1):(\sqrt{5}-1)$

$x+2x+7x={180}^o\Rightarrow x={18}^o$
Hence the angles are ${18}^o,{36}^o,{126}^o$
Greatest side $\infty sin\left({126}^o\right)$
Smallest side $\infty sin\left({18}^o\right)$ and ratio ratio = $\frac{sin{126}^o}{sin\left({18}^o\right)}=\frac{\sqrt{5}+1}{\sqrt{5}-1}.$