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If A, B, C are the angles of a triangle and eiA , eiB , eiC ar e in A.P. Then the trian gle must be
- a)right angled
- b)isosceles
- c)equilateral
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If A, B, C are the angles of a triangle and eiA , eiB , eiC ar e in A....
Squaring and adding we get
cos( A - C) = 1 ⇒ A - C = 0
∴ A = C, From (i) and (ii) cos B = cos A and sin B = sin A
So, A = B.
⇒ A = B = C
Most Upvoted Answer
If A, B, C are the angles of a triangle and eiA , eiB , eiC ar e in A....
Triangle with angles in AP
Triangles have three angles. Let's denote the angles of the triangle as A, B, and C. Given that the angles eiA, eiB, and eiC are in an arithmetic progression (AP).
Properties of a triangle
In a triangle, the sum of the three angles is always 180 degrees. Therefore, we can write the sum of the angles in terms of A, B, and C:
A + B + C = 180
Angles in AP
If the angles eiA, eiB, and eiC are in AP, this implies that:
eiB = (eiA + eiC) / 2
Equilateral triangle
In an equilateral triangle, all three angles are equal. If we assume that the triangle is equilateral, then A = B = C.
Substitute A = B = C into the equation A + B + C = 180, we get:
3A = 180
A = 60
Since A = B = C, all angles are 60 degrees, which satisfies the condition of angles being in AP.
Therefore, the triangle must be equilateral if the angles are in an arithmetic progression.
Triangles have three angles. Let's denote the angles of the triangle as A, B, and C. Given that the angles eiA, eiB, and eiC are in an arithmetic progression (AP).
Properties of a triangle
In a triangle, the sum of the three angles is always 180 degrees. Therefore, we can write the sum of the angles in terms of A, B, and C:
A + B + C = 180
Angles in AP
If the angles eiA, eiB, and eiC are in AP, this implies that:
eiB = (eiA + eiC) / 2
Equilateral triangle
In an equilateral triangle, all three angles are equal. If we assume that the triangle is equilateral, then A = B = C.
Substitute A = B = C into the equation A + B + C = 180, we get:
3A = 180
A = 60
Since A = B = C, all angles are 60 degrees, which satisfies the condition of angles being in AP.
Therefore, the triangle must be equilateral if the angles are in an arithmetic progression.
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If A, B, C are the angles of a triangle and eiA , eiB , eiC ar e in A.P. Then the trian gle must bea)right angledb)isoscelesc)equilaterald)None of theseCorrect answer is option 'C'. Can you explain this answer?
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