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  • If ABC is a triangle and AB=2,  then what is the maximum possible value of A?<div class='qna-optio

If ABC is a triangle and AB=2, BC=\sqrt3 then what is the maximum possible value of A?

Option: 1

\frac{\pi}{3}


Option: 2

\frac{\pi}{4}


Option: 3

\frac{\pi}{6}


Option: 4

\frac{\pi}{2}


Answers (1)

Basic relation b/w sides and angle of triangle and Sine Rule -

Basic relation b/w sides and angle of triangle and Sine Rule

 

 In ΔABC, the angles are denoted by capital letters A, B and C and the length of the sides opposite to these angles are denoted by small letters a, b and c respectively.

 

\mathrm{\begin{array}{l}{ \angle B A C=A} \\ { \angle A B C=B} \\ { \angle B C A=C}\end{array}}

 

Sides of the ΔABC

AB = c, AC = b, and  BC = a

Collectively, these relationships are called the Law of Sines

 

\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}

-

 

\frac{AB}{\sin C}=\frac{BC}{\sin A}\\ \frac{2}{\sin C}=\frac{\sqrt{3}}{\sin A}\\ \sin A= \frac{\sqrt{3}}{2} \sin C\\ \text {maximum possible value of A }=\frac{\pi}{3}

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Kshitij

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