QJEEM19Ma2ccd: JEE Main 2019 Mathematics - Class 11 JEEM19Ma2ccd Solution: With the usual notation, in ABC, if = 120 o , a = 1, b = 1 then …

Question

Verified Solution • 2025–26 Session moderate

With the usual notation, in

\Delta

ABC, if

\angle A + \angle B

= 120^o, a =

\sqrt 3

+

1, b =

\sqrt 3

-

1 then the ratio

\angle A:\angle B,

is :

Accepted Answer

A + B = 120^o

JEE Main 2019 (Online) 10th January Evening Slot Mathematics - Properties of Triangle Question 27 English Explanation

\tan {{A - B} \over 2} = {{a - b} \over {a + b}}\cot \left( {{c \over 2}} \right)

= {{\sqrt 3 + 1 - \sqrt 3 + 1} \over {2\left( {\sqrt 3 } \right)}}\cot \left( {{{30}^o}} \right) = {1 \over {\sqrt 3 }}.\sqrt 3 = 1

{{A - B} \over 2} = {45^o}

\Rightarrow A - B = {90^o}

\ A + B = {120^o}

2A = {210^o}

A = {105^o}

B = {15^o}

\therefore

\angle A:\angle B,

= 7 : 1

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