(B) Given $A = 30^{\circ}$,$a = 7$,and $b = 8$. Calculate $b \sin A = 8 \sin 30^{\circ} = 8 \times 0.5 = 4$. Since $b \sin A < a < b$ (i.e.,$4 < 7 < 8

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(B) Given $A = 30^{\circ}$,$a = 7$,and $b = 8$. Calculate $b \sin A = 8 \sin 30^{\circ} = 8 \times 0.5 = 4$. Since $b \sin A Therefore,there are two possible values for angle $B$,which means there are two solutions.

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

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If $A = 30^{\circ}$,$a = 7$,and $b = 8$ in $\Delta ABC$,then $B$ has

A
One solution
B
Two solutions
C
No solution
D
None of these

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Trigonometrical Equations

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Relation between sides and angles, Solutions of triangles

The area of triangle $ABC$,in which $a = 1$,$b = 2$,and $\angle C = 60^\circ$ is

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If the angles of a triangle are in the ratio $4:1:1$,then the ratio of the longest side to its perimeter is

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In $\triangle ABC$,if $\frac{1}{a+b} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $\sin A$ is equal to

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In a $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then the ratio $a : b$ is:

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If $A = 30^{\circ}$,$a = 7$,and $b = 8$ in $\Delta ABC$,then $B$ has

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The area of triangle $ABC$,in which $a = 1$,$b = 2$,and $\angle C = 60^\circ$ is

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