So I have a right angled triangle as shown in the image 
What I have to prove is that the angle C is not 60 degrees. I am not sure if I have to use Pythagoras theorem or something else.
P.S Please bear with my strange drawing skills.
2026-04-23 14:26:21.1776954381
How to prove one angle is not 60 degree
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A right triangle with a 60 degree angle would be half an equilateral triangle. Hence $BC$ would be half as long as $AC$, so $AC=8$. But $7^2+4^2\ne 8^2$ so indeed Pythagoras tells us that this is not the case.