
02262021, 03:16 PM #61


02262021, 04:05 PM #62
Hello CORONA VIRUS,
There is not enough known about your triangle 3. None of the sides are known without first solving triangle 4 in the following picture and if you solve triangle 4, you don't need triangle 3. Triangle 3's acute angle will be half the combination of the acute angels of your first two triangles, but I doubt that would jump out at the OP. The compliment of the acute angle of triangle 3 would be known, of course, so you would have three angles and no sides; how does that work?
Regards,
Bill

02262021, 04:25 PM #63

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02262021, 04:36 PM #64

02262021, 05:01 PM #65
Unfortunately they do not teach coordinate geometry along with trig.
Start by assigning the X and Y coordinates to all the points you can.
The center of the circle is at x=1,y=1.75
The top of the vertical line at the right is at x=3,y=0.5
The terns deltaX and deltaY are the difference in X and in Y for the ends of a line.
Draw a line from the center of the circle to the top of the vertical line.
The length of the line is: (deltaX)^2 + (deltaY)^2 =Line^2
The slope of the line is: Tan(a) = (deltaY) / (deltaX)
That leaves one right triangle to solve. The hypotenuse is the length of the line just found. The altitude is 1.25.
Use the Pythagorean theorem to find the length of the sloping side of the figure.
The sine of the acute angle in that triangleis: sin(b) = 1.25/hypotenuse.
The line found earlier is the hypotenuse of the triangle.
The slope of the angled line in the figure is angle a + angle b. Call it angle c.
The deltaX and deltaY if the sloping side of the figure are found as follows:
Delta Y = Sloping side * sin(c), delta X = sloping side * cos(c)
By using coordinate geometry there is only one right triangle to solve with trig.


02262021, 07:05 PM #66
Isn't this the same as post #4 and three triangles?
"The length of the line is: (deltaX)^2 + (deltaY)^2 =Line^2" is solving a side right triangle (green) as is "Delta Y = Sloping side * sin(c), delta X = sloping side * cos(c)" (magenta).
Just a different way of saying it.
I see four trig functions needed. Angle A, angle B and then the two sides of the end delta triangle.
Racking my brain for a way with no trig functions and only squared and square roots. Sine, cosine, tangent and the inverses computational expensive but also is square root.
The OP's teacher went for offsets from the Rad center instead but same/same type solution.
To me flipping or mirroring that green triangle in post 4 helps make more sense.
We are all ending up solving the same things with the same math just different pictures.
My first thought was green triangle not needed as line length easy but picture wise that is how it is solved.
PDF linked here I hope. Coordinate system has to be moved to a new zero/zero but that just easy addition and subtraction transform.
https://www.google.com/url?sa=t&rct=...OOf9WVHDowNImy
For more fun assume the part has 23 degrees positive rake on X and 15 degrees positive in Y so is tipped and twisted in the machine vise to machine axis so the end mill can cut it although the print is flat plane inspection.
Lots more triangles.
Bob

02272021, 08:29 PM #67
As Bob has mentioned, its a different way of saying it.
There are quite a few ways of solving the OP's problem; I stated as much in my first post. There are some methods that require higher math skills, but this Thread is about identifying the triangles to use with Trig to get the answer.
The method Bob posted the link uses no Trig whatsoever and is a derivative of calculating the intersection points of two circles, with the second circle radius being the length of the line tangent to the first circle. A visual representation of the solution is shown in the following picture:
In the above, the calculations relating to the triangles are all pythagoras theorem based.
Regards,
Bill

02272021, 08:59 PM #68
man, you guys are smart. Haha. I hope to understand this stuff remotely as well at some point.
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02272021, 09:09 PM #69


02272021, 09:13 PM #70
Two engineering students meet on a bike path. Hey, nice new bike. Yeah, that coed that was all over me ran into me on the wooded shortcut. She got off her bike and took off all of her clothes and said "take what ever you want". Other engineer "good choice, her clothes prob would not fit you well at all".

02272021, 09:15 PM #71

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02272021, 09:15 PM #72
So many ways to skin the cat.
What is the best to teach?
I still think angelw's post four nailed it but I would have flipped the green as easier to get if underneath.
While a perfectly fine and same solution to the teacher I would not have gone for the top triangles.
IMO harder to understand.
Despite some poking done in the past for sure Bill is a wiz and true math magician at this stuff. Wonder what conversations in real life are like?
Does it go to where the wives just say "We will cook the hot dogs and burgers and you can talk things that make no sense at all".
Bob

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02272021, 09:24 PM #73
First couple weeks in Trig, I immediately saw the application of basic sin/cosine for ...
Hole patterns! I can calculate X and Y coordinates with this!
Beyond that, I was pretty well lost. Never mind he taught it 'wrong'. I guess to make it easy he showed us a regular triangle on the blackboard, and 'the sin is the Y value, and the cosine is the X value.'
Made it tough to figure things out without turning the drawing around on the bench, or trying to imagine what it looked like from the other side. I never could figure out what the hell my Dad was talking about with all the 'opposite over adjacent' crap ...
Goddam 'New Math'. 45 years later it still screws me up.

02282021, 02:43 AM #74
Hello Bob,
Wife? What wife?
An engineer crosses a road when a frog calls out to him, “If you kiss me, I’ll turn into a beautiful princess.”
He bends over, picks up the frog, but instead of kissing it he puts it in his pocket. The frog, perplexed, upped the ante. “If you kiss me and turn me back into a beautiful princess, I will stay with you for one month.” The engineer took the frog out again, considered it, but put it back again ino his pocket.
The frog, growing desperate, cries out, “If you kiss me and turn me back, I’ll do whatever you say!” Again the engineer takes the frog out, smiles at it, and puts it back into his pocket.
Finally, the frog asks, “What is the matter? I’ve told you I’m a beautiful princess, I’ll stay with you for a month and do whatever you say. What more do you want?”
The engineer says, “Look, I’m an engineer. I don’t have time for a girlfriend, but a talking frog, now that’s cool!”
Regards,
Bill

03012021, 09:25 AM #75
I think that this needs posted here:
I don't know about the rest of y'all, but I was taught 40 yrs ago that triangles had 180*, and all of our werk was based on that principal.
However, I finally saw the error of my mentor's ways, and now realize that there is 270*, and have now had to go back and recalculate a LOT of work!

Think Snow Eh!
Ox

03012021, 10:12 AM #76
https://youtu.be/ro1I03ktSa4
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03012021, 10:28 AM #77

03012021, 03:51 PM #78

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03012021, 08:10 PM #79

03022021, 02:08 AM #80
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