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AP EAMCET · Maths · Properties of Triangles

In \(\triangle A B C, \angle B=60^{\circ}\) and \(\angle A=75^{\circ}\). If a point \(D\) divides \(\mathrm{BC}\) in the ratio \(2: 3\), then \(\sin \angle \mathrm{BAD}: \sin \angle \mathrm{CAD}=\)

  1. A \(\sqrt{2} ; \sqrt{3}\)
  2. B \(\sqrt{3}: 2\)
  3. C \(\sqrt{3}: \sqrt{2}\)
  4. D \(3: \sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{2} ; \sqrt{3}\)

Step-by-step Solution

Detailed explanation

Given \(\angle B=60^{\circ}, \angle A=75^{\circ}\) Let \(\angle B A D=\theta\) and \(\angle C A D=\phi\) Using sine rule in \(\triangle A B D\), \(\frac{A D}{\sin 45^{\circ}}=\frac{C D}{\sin \phi}\) ...(ii) Also, given \(\frac{B D}{C D}=\frac{2}{3}\) Now, Eqn. (i)/(ii),…