Question : In a $\triangle ABC, \angle B=\frac{\pi}{3}, \angle C=\frac{\pi}{4}$ and D divides BC internally in the ratio 1 : 3, then $\frac{\sin \angle BAD}{\sin \angle CAD}$ is equal to:
Option 1: $\frac{1}{\sqrt{2}}$
Option 2:
$\frac{1}{\sqrt{3}}$
Option 3:
$\frac{1}{\sqrt{6}}$
Option 4: $\sqrt{6}$
Correct Answer:
$\frac{1}{\sqrt{6}}$
Solution :
Given:
$\triangle ABC, \angle B=\frac{\pi}{3}=\frac{180°}{3}=60°,$ and $\angle C=\frac{\pi}{4}=\frac{180°}{4}=45°$
So, $\angle A= 180°-(60°+45°)=75°$
In triangles $ABD$ and $ACD$, we have:
$\frac{AB}{\sin B}=\frac{BD}{\sin \angle BAD}$ and
$\frac{AD}{\sin C}=\frac{CD}{\sin \angle CAD}$
⇒ $\frac{\sin C}{\sin B}=\frac{\sin \angle CAD}{\sin \angle BAD}×\frac{BD}{CD}$
⇒ $\frac{\sin 60°}{\sin 45°}=\frac{\sin \angle CAD}{\sin \angle BAD}×\frac{1}{3}$
⇒ $\frac{\sin \angle BAD}{\sin \angle CAD}=\frac{1}{3}×\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}=\frac{1}{\sqrt{6}}$
Hence, the correct answer is $\frac{1}{\sqrt{6}}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
