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If in a triangle, the angles are in A.P. and b: c = 3:2, then A is equal to - Mathematics and Statistics

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Question

If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to

Options

  • 30°

  • 60°

  • 75°

  • 45°

MCQ
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Solution

If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to 75°.

Explanation:

`angle"B"` = 60° `angle"A"` + `angle"C"` = 120

Now,

`b/c = sqrt3/sqrt2 = sin B/sin A`

sin C = `1/sqrt2`

`angle"C"` = 45°

Hence, `angle"A"` = 75°

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Trigonometric Equations and Their Solutions
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Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 107]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 1.10 | Page 107

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