Question

In a right triangle if Hypotenuse is H , perpendicular is P and base is B , then​

Answer 1

${(H)}^{2} = {(P)}^{2} + {(B)}^{2} \\ {(P)}^{2} = {(H)}^{2} - {(B)}^{2} \\ {(B)}^{2} = {(H)}^{2} - {(P)}^{2}$

Answer 2

Given :  In a right triangle if Hypotenuse is H , perpendicular is P and base is B

To Find : Relation between H . P and B

Solution:

Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal   to the sum of the squares of the other two perpendicular sides.

P²+B²=H²  

in ΔABC right angled at C

BC = Base = B  

AC = Perpendicular = P

AB = Hypotenuse = H

Proof

Sin B = AC/AB  = P/H

CosB = BC/AB  = B/H

Sin²B + Cos²B = 1

=> (P/H)² + (B/H)² = 1

=> P²/H² + B²/H² = 1

=> P² + B² = H²

QED

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