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If b,c and sinB are given such that ∠B is acute and b<c sinB, then
- a)No triangle is possible
- b)One triangle is possible
- c)Two triangle are possible
- d)One right angled triangle is possible
Correct answer is option 'A'. Can you explain this answer?
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If b,c and sinB are given such that ∠B is acute and b<c sinB, t...
When two sides and angle opposite to one of then be given. In this case, the triangle is not always uniquely determined. It is quite possible to have no triangle, one triangle and two triangles with this type of data.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b2 = c2 + a2 - 2ac cos B
⇒ a2 - 2ac cos B = b2 - c2
⇒ a2 - 2ac cos B + c2 cos2 B
= b2 - c2 + c2 cos2 B
⇒ (a - c cos B)2 = b2 - c2 (1 - cos2 B)
= b2 - c2 sin2 B
This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no solution.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b2 = c2 + a2 - 2ac cos B
⇒ a2 - 2ac cos B = b2 - c2
⇒ a2 - 2ac cos B + c2 cos2 B
= b2 - c2 + c2 cos2 B
⇒ (a - c cos B)2 = b2 - c2 (1 - cos2 B)
= b2 - c2 sin2 B
This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no solution.
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If b,c and sinB are given such that ∠B is acute and b<c sinB, thena)No triangle is possibleb)One triangle is possiblec)Two triangle are possibled)One right angled triangle is possibleCorrect answer is option 'A'. Can you explain this answer?
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If b,c and sinB are given such that ∠B is acute and b<c sinB, thena)No triangle is possibleb)One triangle is possiblec)Two triangle are possibled)One right angled triangle is possibleCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If b,c and sinB are given such that ∠B is acute and b<c sinB, thena)No triangle is possibleb)One triangle is possiblec)Two triangle are possibled)One right angled triangle is possibleCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If b,c and sinB are given such that ∠B is acute and b<c sinB, thena)No triangle is possibleb)One triangle is possiblec)Two triangle are possibled)One right angled triangle is possibleCorrect answer is option 'A'. Can you explain this answer?.
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