Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleAmbiguous case of triangleMedium2 minQB

MathematicsMediummultiple choice

There exists a triangle ABC satisfying the conditions

Options:(select one or more)

Answer:

A, D

Solution:

The sine formula is $\frac{a}{s i n A} = \frac{b}{s i n B} \Rightarrow$ $a sin Bb sin A$ cohice (A) $b sin A = a \Rightarrow a sin B = a \Rightarrow B = p /2$

$∴ ∠ A < \frac{π}{2}$

∴ the triangle is possible Choice (b) and (c) $b sin A > a a sin B > a sin B > 1$

∴ DABC is not possible. choice

(D) $b sin A < a \Rightarrow a sin B < a \Rightarrow sin B < 1$ $\Rightarrow ∠ B$ does exist Now, if $b > a \Rightarrow B > A ∴ A < p /2$

∴ the triangle is possible

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Ambiguous case of triangle

⏱ 2mℹ️ Source: QB

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