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Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =
- a)(11/290)
- b)(√11/290)
- c)(-11/√290)
- d)-(√11/290)
Correct answer is option 'C'. Can you explain this answer?
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Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =...
Given,
Vertices of a ΔABC are (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =
From figure,
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Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =...
Understanding the Triangle Vertices
The vertices of the triangle are given as A(0,0), B(2,-1), and C(9,2). We need to find cosB, where B is the angle at vertex B.
Calculating the Lengths of the Sides
- AB (from A to B):
- Length = √[(2-0)² + (-1-0)²] = √(4 + 1) = √5
- BC (from B to C):
- Length = √[(9-2)² + (2-(-1))²] = √(49 + 9) = √58
- AC (from A to C):
- Length = √[(9-0)² + (2-0)²] = √(81 + 4) = √85
Using the Cosine Rule
The cosine of angle B can be calculated using the cosine rule:
cosB = (AB² + BC² - AC²) / (2 * AB * BC)
Substituting the Lengths
- AB² = 5
- BC² = 58
- AC² = 85
Now substitute into the cosine formula:
cosB = (5 + 58 - 85) / (2 * √5 * √58)
This simplifies to:
cosB = (-22) / (2 * √5 * √58) = -11 / (√290)
Conclusion
Thus, the correct answer is option 'C': -11/√290, indicating that angle B is obtuse, as the cosine is negative.
The vertices of the triangle are given as A(0,0), B(2,-1), and C(9,2). We need to find cosB, where B is the angle at vertex B.
Calculating the Lengths of the Sides
- AB (from A to B):
- Length = √[(2-0)² + (-1-0)²] = √(4 + 1) = √5
- BC (from B to C):
- Length = √[(9-2)² + (2-(-1))²] = √(49 + 9) = √58
- AC (from A to C):
- Length = √[(9-0)² + (2-0)²] = √(81 + 4) = √85
Using the Cosine Rule
The cosine of angle B can be calculated using the cosine rule:
cosB = (AB² + BC² - AC²) / (2 * AB * BC)
Substituting the Lengths
- AB² = 5
- BC² = 58
- AC² = 85
Now substitute into the cosine formula:
cosB = (5 + 58 - 85) / (2 * √5 * √58)
This simplifies to:
cosB = (-22) / (2 * √5 * √58) = -11 / (√290)
Conclusion
Thus, the correct answer is option 'C': -11/√290, indicating that angle B is obtuse, as the cosine is negative.
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Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer?.
Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer?.
Solutions for Points (0,0), (2,-1) and (9,2) are vertices of a triangle, then cosB =a)(11/290)b)(√11/290)c)(-11/√290)d)-(√11/290)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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