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If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter. If ∠BOC = 54°, then ∠BAC is
- a)108°
- b)126°
- c)136°
- d)116°
Correct answer is option 'B'. Can you explain this answer?
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If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is ...
Understanding the Triangle Properties
In triangle ABC, angle A is obtuse. The orthocenter O is the intersection of the altitudes from each vertex. Given that angle BOC is 54°, we need to find angle BAC.
Relationship Between Angles
- The angle BOC can be expressed in terms of angle A:
- Angle BOC = 180° - angle A
Calculating Angle A
- Given angle BOC = 54°, we set up the equation:
- 180° - angle A = 54°
- Rearranging gives:
- angle A = 180° - 54° = 126°
Conclusion
- Since angle A is obtuse (greater than 90°), the calculated angle A = 126° is valid.
Thus, angle BAC is 126°, which corresponds to option 'B'.
Summary
- Angle A (BAC) of obtuse triangle ABC is found using the relationship with angle BOC.
- With BOC = 54°, we determine:
- angle A = 126°.
Therefore, the answer is option 'B' - 126°.
In triangle ABC, angle A is obtuse. The orthocenter O is the intersection of the altitudes from each vertex. Given that angle BOC is 54°, we need to find angle BAC.
Relationship Between Angles
- The angle BOC can be expressed in terms of angle A:
- Angle BOC = 180° - angle A
Calculating Angle A
- Given angle BOC = 54°, we set up the equation:
- 180° - angle A = 54°
- Rearranging gives:
- angle A = 180° - 54° = 126°
Conclusion
- Since angle A is obtuse (greater than 90°), the calculated angle A = 126° is valid.
Thus, angle BAC is 126°, which corresponds to option 'B'.
Summary
- Angle A (BAC) of obtuse triangle ABC is found using the relationship with angle BOC.
- With BOC = 54°, we determine:
- angle A = 126°.
Therefore, the answer is option 'B' - 126°.
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If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter.If ∠BOC = 54°, then ∠BAC isa)108°b)126°c)136°d)116°Correct answer is option 'B'. Can you explain this answer?
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If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter.If ∠BOC = 54°, then ∠BAC isa)108°b)126°c)136°d)116°Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter.If ∠BOC = 54°, then ∠BAC isa)108°b)126°c)136°d)116°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter.If ∠BOC = 54°, then ∠BAC isa)108°b)126°c)136°d)116°Correct answer is option 'B'. Can you explain this answer?.
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