Gemotry of circle and right angle

[quantum_enhan]

ALright, just a quick question concerning this diagram. Since the 90 degree angle is directed along the middle ove the circle, does that mean if you draw a line from where the circle is touching the ninety degree angle to the centre of the circle, it would make a 45 degree angle with the vertical of the centre of the circle and the nine degree angle?

For example, to find x, would I go:

cos 45deg = 2inch/b
b=2.83
thus x = 2.83-0.5 = 2.33

 

[Mentallic]

From the centre to one of the contacts it's 90^o, from the centre to the other point of contact it's 90^o and the 3rd angle given is 90^o, by the sum of quadrilaterals property the last angle is...?

 

[quantum_enhan]

90 degrees. So then the calculations would be correct, would they not? Since the center of the circle is below the metal block, we would just add 0.5 to to answer calculated from the triangle? ps thank u

 

[Mentallic]

Sorry about the late reply. Yes, that's correct. You could also solve it without using any trigonometry as follows:

The height from the ground to the top of the triangle is x+2.5
The height from the centre of the circle to the top of the triangle is - by pythagoras' theorem - $$2\sqrt{2}$$ thus for the total height it is $$2+2\sqrt{2}$$.

Therefore $$2+2\sqrt{2}=x+2.5$$

But really it just switches from using trigonometry to using pythagoras' theorem so it's essentially the same.