Hi chriss2525,
I'll attack the last one.
For this one, connect the 3 centers of the holes and you form an equilateral triangle.
Next, draw a radius from the center of the big circle to a vertex.
Now draw a perpendicular to the base of the triangle.
What you have formed now is a 30-60-90 triangle.
You can find the hypotenuse by taking half the diameter of the big circle.
That would be 162.5.
Using your 30-60-90 rules (or trigonometry, if you prefer), you can determine the apothem of the equilateral triangle.
It's half the hypotenuse or 81.25
Finally, the base of the right triangle that you formed can be determined by a number of different ways:
Pythagorean Theorem
Trigonometry
30-60-90 rules
You should find that length to be $\displaystyle 81.25\sqrt{3}$
Multiply this answer by 2 and you have your desired result.
Here's the 2nd to last one: I edited the diagram and made a right triangle by adding a red line segment, which you can see here:
The length of the green line segment can be found be subtracting 0.400 from 0.930. Then, use the trig definition
$\displaystyle \tan\,\theta = \frac{opp}{adj}$
to find the opposite side. (The red is the opposite side, and the green is the adjacent side.) Once you find the opposite side, subtract that from 2.188 to get y.
For the first one, try redrawing the image, and extend out the slanted edges so that they meet.
Then draw another horizontal from the top of $\displaystyle y$ and another horiztonal from the bottom of $\displaystyle y$.
You should then have two triangles you can solve from angles you can find from "angles in parallel lines" properties.
Hi chriss2525,
If you're still working on these, here's #2:
I drew 2 red vertical lines to the base.
Two right triangles were formed with 45 deg. 50 min angles in them.
I subtracted .250 from .785 to get the height of the right triangles which is .535.
I needed to find the bases of these triangles, so I used a little trigonometry.
$\displaystyle \tan (42\frac{5}{6})=\frac{.535}{b}$
Once I found the bases, I subtracted them from 2.125.
This is the value of x.
$\displaystyle x=2.125-.577-.577$
$\displaystyle x=.971$