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Question

In triangle ABC and triangle XYZ if angle A and angle X are acute angles such that cosA=cosX then show that angle A=angle X


Solution

cos A =cos X

AB/AC =XY/XZ =k

AB =k AC

from Pythagoras theorem,

BC =sqrt( (AC)2 - (AB)2 )

= AC sqrt( 1 - (k)2 )

similarly, YZ =XZ sqrt( 1 - (k)2 )

BC / YZ = AC / XZ ————————1

AC / XZ = AB /XY —————————2

BC / YZ = AC / XZ = AB / XY (by SSS criterion of similarity)

hence proved.

{ HINT : (AC)2 = AC*AC

sqrt = square root }

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