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In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter. If ∠BOC = 54°, then ∠BAC is (SSC CGL 1st Sit. 2012)
- a)108°
- b)126°
- c)136°
- d)116°
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is ...
In an obtuse-angled triangle ABC, the measure of one angle is greater than 90 degrees. This means that angle A, B, or C is greater than 90 degrees.
Let's assume that angle A is greater than 90 degrees. This means that angle B and angle C are acute angles.
In an obtuse-angled triangle, the longest side is opposite the obtuse angle. Let's assume that side BC is the longest side.
Since angle A is greater than 90 degrees, side BC is the longest side and is opposite angle A.
Therefore, in an obtuse-angled triangle, the longest side is opposite the obtuse angle.
Let's assume that angle A is greater than 90 degrees. This means that angle B and angle C are acute angles.
In an obtuse-angled triangle, the longest side is opposite the obtuse angle. Let's assume that side BC is the longest side.
Since angle A is greater than 90 degrees, side BC is the longest side and is opposite angle A.
Therefore, in an obtuse-angled triangle, the longest side is opposite the obtuse angle.
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In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is ...
Let altitudes drawn from vertex B and C cross each other at Point ‘O’.
then, ∠BOC = 54° = ∠EOF {vertically opposite angles}
Now, in quadrilateral AEOF
∠AEO + ∠AFO + ∠EAF + ∠EOF = 360°
90° + 90° + ∠EAF + 54° = 360°
∴ ∠EAF = 360° – 90° – 90° – 54° = 126°
∴ ∠EAF = ∠BAC = 126°
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In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter. If ∠BOC = 54°, then ∠BAC is (SSC CGL 1st Sit. 2012)a)108°b)126°c)136°d)116°Correct answer is option 'B'. Can you explain this answer?
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