6 Views

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: $\sqrt{6}$


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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 $\frac{1}{\sqrt{6}}$.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books