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Question

Consider a right angled triangle ABC, right angled at B. The length of AC is 5 cm, the length of BC is 3 cm and A=37 . The sum of the magnitudes of AB, BC and C is ___

[Magnitude is defined as the absolute value. Example: If A is 60 then, its magnitude is 60; and if length AB=45 cm, then magnitude of AB=45.]

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Solution

Using angle sum property of a triangle, A+B+C=180

C=180AB=1803790=53

Applying Pythagoras theorem,

AB2+BC2=AC2

AB2=AC2BC2=259=16.

AB=4 cm

Thus, magnitude of AB, BC and C=4+3+53=60


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