Given a ΔABC in which B=90 and AB=3BC. Prove that C=60.
B C A


Answer:


Step by Step Explanation:
  1. Let D be the midpoint of the hypotenuse AC.

    Join BD.
    B C A D
  2. Now, we have AC2=AB2+BC2[ By pythagoras' theorem ]AC2=(3BC)2+BC2[ AB = 3 BC (given) ]AC2=4BC2AC=2BC2CD=2BC[ D is the midpoint of AC]CD=BC (i) 
  3. We know that the midpoint of the hypotenuse of a right triangle is equidistant from the vertices.  BD=CD (ii)  From (i) and (ii), we get BC=BD=CD Therefore, ΔBCD is equilateral and hence C=60.

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