Question

Show that in a right angled triangle, thehypotenuse is the longest side.

Answer 1

yeah, hypotenuse is a longest side in a triangle

Answer 2

Step-by-step explanation:

Let us consider a right - angled triangle ABC , right - angled at B ,

In ∆ ABC ,

angle A + angle B + angle C = 180° [ Angle sum property of a triangle ]

angle A + 90° + angle C = 180°

angle A + angle C = 90°

Hence , the other two angles have to be acute [ i.e less than 90° ]

angle B is the largest angle in ∆ABC .

angle B less than angle A and angle B less than angle C

AC less than BC and AC less than AB

[ In any triangle b, the side opposite to the larger ( greater ) angle is longer ] .

Therefore , AC is the largest side in ∆ABC .

However , AC is the hypotenuse of ∆ABC .

Therefore , hypotenuse is the longest side in a right - angled triangle .

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