Hi, I'm taking an online Math course and im really stuck on these couple of questions. My book doesn't even come close to telling me how to solve these. I'f you could please tell me how to solve these than that would be great!!!!
Any help is appreciated.
Thank you very much.

2. Originally Posted by chriss2525
[FONT=Arial][SIZE=3]Hi, I'm taking an online Math course and im really stuck on these couple of questions. My book doesn't even come close to telling me how to solve these. I'f you could please tell me how to solve these than that would be great!!!!
Any help is appreciated.
Thank you very much.

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 $81.25\sqrt{3}$

3. wow, Thats amazing! i would have never have thought of that. Thanks a lot for answering that last question! Now i just need to se if anyone else will answer my other ones.

4. 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
$\tan\,\theta = \frac{opp}{adj}$
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.

5. 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 $y$ and another horiztonal from the bottom of $y$.

You should then have two triangles you can solve from angles you can find from "angles in parallel lines" properties.

6. Originally Posted by chriss2525
Hi, I'm taking an online Math course and im really stuck on these couple of questions. My book doesn't even come close to telling me how to solve these. I'f you could please tell me how to solve these than that would be great!!!!
Any help is appreciated.
Thank you very much.

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.

$\tan (42\frac{5}{6})=\frac{.535}{b}$

Once I found the bases, I subtracted them from 2.125.

This is the value of x.

$x=2.125-.577-.577$

$x=.971$

7. Yes i am still working on them. Thats great Masters Thanks a lot for you're help it'll for sure help me outon my final exam in 2 weeks!