Trigonometric Equations Question 215
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
Options:
A) $ 1:2 $
B) 2 :1
C) $ (\sqrt{5}+1):(\sqrt{5}-1) $
D) $ (\sqrt{5}-1):(\sqrt{5}+1) $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ x+2x+7x=180^{o}\Rightarrow x=18^{o} $ Hence the angles are $ 18^{o},36^{o},126^{o} $ Greatest side $ \propto $ $ \sin (126^{o}) $ Smallest side $ \propto $ $ \sin (18^{o}) $ and ratio $ =\frac{\sin 126^{o}}{\sin (18^{o})}=\frac{\sqrt{5}+1}{\sqrt{5}-1} $ .
BETA
