Trigonometric Equations Question 277
Question: If the angles of a triangle are in the ratio 4:1:1, then the ratio of the longest side to the perimeter is
[IIT Screening 2003]
Options:
A) $ \sqrt{3}:(2+\sqrt{3}) $
B) $ 1:6 $
C) $ 1:(2+\sqrt{3}) $
D) $ 2:3 $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ 4x+x+x=180{}^\circ \Rightarrow 6x=180{}^\circ \Rightarrow x=30{}^\circ $ $ \frac{\sin 120^{o}}{a}=\frac{\sin 30^{o}}{b}=\frac{\sin 30^{o}}{c} $
$ \therefore a:(a+b+c)=(\sin 120^{o}):(\sin 120^{o}+\sin 30^{o}+\sin 30^{o}) $ $ =\frac{\sqrt{3}}{2}:\frac{\sqrt{3}+2}{2}=\sqrt{3}:\sqrt{3}+2. $
BETA
