(D) Given $b = 3, c = 4$ and $B = \frac{\pi}{3}$.We calculate $c \sin B = 4 \sin \frac{\pi}{3} = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}$.Since $\sqrt

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(D) Given $b = 3, c = 4$ and $B = \frac{\pi}{3}$.We calculate $c \sin B = 4 \sin \frac{\pi}{3} = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}$.Since $\sqrt{3} \approx 1.732$,we have $2\sqrt{3} \approx 3.464$.Comparing this with $b$,we find $c \sin B = 2\sqrt{3} > 3 = b$.Since $b Therefore,no triangle can be constructed.

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

Medium

If $b = 3, c = 4$ and $B = \frac{\pi}{3}$,then the number of triangles that can be constructed is

A
Infinite
B
Two
C
One
D
Nil

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Relation between sides and angles, Solutions of triangles

In $\triangle ABC$,$a^2 \sin 2B + b^2 \sin 2A =$

EasyAP EAMCET 2024

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If two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^{\circ}$. If the third side is $3$,then the remaining fourth side is :-

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If $a^2, b^2, c^2$ are in $A.P.$,then which of the following are also in $A.P.$?

Medium

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What is the greatest angle of the triangle whose sides are $x^2+x+1, 2x+1, x^2-1$ (in $^{\circ}$)?

DifficultAP EAMCET 2021

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If in the $\Delta ABC$,$AB = 2BC$,then find the ratio $\tan \frac{B}{2} : \cot \left( \frac{C - A}{2} \right)$.

Medium

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If $b = 3, c = 4$ and $B = \frac{\pi}{3}$,then the number of triangles that can be constructed is

Similar Questions

In $\triangle ABC$,$a^2 \sin 2B + b^2 \sin 2A =$

If two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^{\circ}$. If the third side is $3$,then the remaining fourth side is :-

If $a^2, b^2, c^2$ are in $A.P.$,then which of the following are also in $A.P.$?

What is the greatest angle of the triangle whose sides are $x^2+x+1, 2x+1, x^2-1$ (in $^{\circ}$)?

If in the $\Delta ABC$,$AB = 2BC$,then find the ratio $\tan \frac{B}{2} : \cot \left( \frac{C - A}{2} \right)$.

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