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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