WIth the usual notation, in  \Delta ABC,  if \angle A + \angle B = 120^{\circ}, a = \sqrt3 +1 and b = \sqrt3 -1, then the ratio\angle A : \angle B , is:

  • Option 1)

    3:1

  • Option 2)

    7:1

  • Option 3)

    9:7

  • Option 4)

    5:3

Answers (1)
A admin

 

Addition Formulae -

\sin \left ( A+B \right )= \sin A\cos B+\cos A\sin B

- wherein

A and B are two angles.

Given \angle A+\angle B=120^{\circ}.........................(1)

from the concept

\tan (\frac{A-B}{2})=\frac{a-b}{a+b}\cot\frac{C}{2}

                           =\frac{\sqrt 3+1-\sqrt 3+1}{2\sqrt 3}\cot30^{\circ}

                          =1

\because \tan 45^{\circ}=1

So,

\frac{A-B}{2}=45

=>A-B=90..........................(2)

From (1) and (2)

=>A=105^{\circ},B=15^{\circ}

 

 

 


Option 1)

3:1

Option 2)

7:1

Option 3)

9:7

Option 4)

5:3

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