Question

OTHER THAN USING TRIGONOMETRY

Answer 1

solution:

For triangle having 45,45 and 90 as are the ratio

1:1:root 2

Note: in the below answer I have taken BC as 1 as it is the side opposite to 30 degree

second way,

( the figure is in the attachment) (second figure)

Draw a median CD to AB from C.

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.

angle C = 60°