if each angle of a triangle is less than the sum of the other two,show that the triangle is acute angle
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Let a, b and c be three angles of a triangle. Then, a+b+c =180° ……….(1)
If a+b <c, then using equation (1), we get;
c+c < 180° => 2c <180° => c <180°/2
=> c < 90°
Similarly, we get; a<90° and b<90°
=> Each angle of the triangle is less than 90° and hence it is an acute angled triangle.
If a+b <c, then using equation (1), we get;
c+c < 180° => 2c <180° => c <180°/2
=> c < 90°
Similarly, we get; a<90° and b<90°
=> Each angle of the triangle is less than 90° and hence it is an acute angled triangle.
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