Question

ABC is a right triangle right angled at C and AC= root 3BC prove that angle BAC=60degree​

Answer 1

Draw a median CD to AB from C.[diagram in the attachment}

Now, by Pythagoras theorem in ABC, AB=2*BC.

Thus, BD= half of AB = BC.

But, the point of bisection of the hypotenuse is equidistant from all sides.

Thus, CD=BD=AD.

That implifies, CD=BD=BC.

Thus, CDB is an equilateral triangle.

Therefore, angle DBC = angle ABC = 60 degrees.

NOTE-This is the answer if looking for a method without using trigonometry.