Question

In triangle MNP,if angle N is 90°, then prove MP2=MN2+NP2.​

Answer 1

Given : In triangle MNP,if angle N is 90°,

To prove :  MP²= MN²+NP²​

Solution:

MNP  is right angled triangle at N

Sin ( angle) = Perpendicular / hypotenuse

Sin ∠M   =  NP/MP

Cos ( angle) =Base / hypotenuse

Cos ∠M  =  MN/MP

Sin² M  + Cos² M  = 1

=> (NP/MP)² + (MN/MP)² = 1

=> NP² + MN² = MP²

=> MP²  = MN² + NP²

QED

Hence proved

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