JEE Main 2019MathematicsProperties of TrianglesHardMCQ

JEE Main 2019 — Properties of Triangles Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

With the usual notation in ∆ABC, if ∠A+∠B=120°, a=3+1 units and b=3-1 units, then the ratio ∠A:∠B is

Choose an option

Show full solutionCorrect option: A
Correct answer
A7:1

Step-by-step explanation

Let angle B is x.

Using sine rule, we get

3+1sin120°-x=3-1sinx.

⇒3+13-1=sin120°-xsinx

⇒3+13-1=sin120°cosx-cos120°sinxsinx

⇒3+13-1=sin120°cotx-cos120°

⇒3+13-1-12=32cotx

⇒3+232=32cotx

⇒cotx=3+2

⇒tanx=2-3

⇒x=∠B=15°

⇒120-x=∠A=105°

⇒∠A:∠B=7:1

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About this question

This is a previous-year question from JEE Main 2019, covering the Properties of Triangles chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.