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AIEEE 2003

JEE Main 2003 Mathematics question on Trigonometry

If the angles of a triangle are in the ratio 4:1:14:1:1, then the ratio of the longest side to the perimeter is
  1. A.
    3:(2+3)\sqrt{3} : (2+\sqrt{3})
  2. B.
    1:3:21:3:2
  3. C.
    1:2+31:2+\sqrt{3}
  4. D.
    2:32:3
Show answer and solution

Correct option: A

Solution

The angles are 4:1:1, summing to 180°, giving angles 120°, 30°, 30°.

By the sine rule, sides are proportional to sin(120°), sin(30°), sin(30°) = (√3/2), (1/2), (1/2).

Longest side : perimeter = (√3/2) : (√3/2 + 1/2 + 1/2) = √3 : (√3 + 2) = √3 : (2 + √3).

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