Question

a) If each angle of a triangle is less than the sum of the other two, show that the triangle is acute
angled
(Hint. Let ZA <ZB + 2C then 2ZA<ZA + 2B + ZC = 2ZA < 180° ZA < 90°
Similarly, ZB < 90° and 2C< 90°]​

Answer 1

Answer:

Let ∠A ∠B and ∠C be the interior angles of ΔABC

Each angle is less than the sum of the other two angles (given)

Consider ∠A < ∠B + ∠C

=> ∠A < 180° - ∠A [∠A + ∠B + ∠C = 180°]

=> 2 ∠A < 180°

=> ∠A < 90°

So ∠A is an acute angle

ΔABC is an obtuse angled triangle.

Answer 2

Answer:

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