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Standard XII

Mathematics

Principal Solution of Trigonometric Equation

In Δ ABC ...

Question

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
If $b = c s i n B$ , then the triangle is?

Equilateral

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Right Angled

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Acute Angled

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Obtuse Angled

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Solution

The correct option is C Right Angled
Using the Sine rule, we have $\frac{b}{s i n B} = \frac{c}{s i n C}$
$b = C s i n B$ (given)
$\to s i n C = 1$
Thus $C = \frac{π}{2}$
$∴$ the given triangle is a right angle triangle.

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Similar questions

Δ

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In Δ ABC the sides opposite to angles A,B,C are denoted by a,b,c respectively.If b=csinB, then the triangle is?

The correct option is C Right AngledUsing the Sine rule, we have bsin B=csin Cb=C sin B (given)→sin C=1Thus C=π2∴ the given triangle is a right angle triangle.

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
If $b = c s i n B$ , then the triangle is?

The correct option is C Right Angled
Using the Sine rule, we have $\frac{b}{s i n B} = \frac{c}{s i n C}$
$b = C s i n B$ (given)
$\to s i n C = 1$
Thus $C = \frac{π}{2}$
$∴$ the given triangle is a right angle triangle.