MHB Trig Assistance for CNC Machining/Engineering

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The discussion centers around solving trigonometric equations related to CNC machining and engineering, focusing on the relationships between diameters and similar triangles. Key equations include $dR = \frac{39}{\sin y}$, $cr = \frac{23.5}{\sin y}$, and $ch = \frac{86}{\tan y}$, leading to the equation $126 = \frac{39}{\sin y} + \frac{23.5}{\sin y} + \frac{86}{\tan y}$. Participants clarify terms like "DIA" for diameter and address potential gaps in the diagram affecting calculations. The conversation also touches on the appropriateness of outside help for educational purposes, confirming that the inquiry is for developing a revision workbook for engineering students.
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Trig help please! CNC Machining/Engineering

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I redraw the picture. you mean by DIA ( diameter ) right ?. you can notice that the two triangles the one with the big circle and the one with small circle are similar.

$dR = \frac{39}{\sin y}, cr = \frac{23.5}{\sin y}, ch = \frac{86}{\tan y}$ now

$dR + cr + ch = 126 $ hence

$126 = \frac{39}{\sin y} + \frac{23.5}{\sin y} + \frac{86}{\tan y} $

$126 \sin y = 62.5 + 86 \cos y $
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Yes DIA means the diameter...
 
Amer said:
I redraw the picture. you mean by DIA ( diameter ) right ?. you can notice that the two triangles the one with the big circle and the one with small circle are similar

Sorry your picture is not working now.
 
I edited my post
 
Amer said:
I redraw the picture. you mean by DIA ( diameter ) right ?. you can notice that the two triangles the one with the big circle and the one with small circle are similar.

$dR = \frac{39}{\sin y}, cr = \frac{23.5}{\sin y}, ch = \frac{86}{\tan y}$ now

$dR + cr + ch = 126 $ hence

$126 = \frac{39}{\sin y} + \frac{23.5}{\sin y} + \frac{86}{\tan y} $

$126 \sin y = 62.5 + 86 \cos y $

Just not too sure with the distance from S - H?
 
megani said:
Just not too sure with the distance from S - H?
you mean ch ? it is typo I meant $dh$. ch is perpendicular to SR so we have a right triangle $\tan y = \frac{86}{hd} $
$hd + dR + cr = 126$
 
Yes sorry HD...Initially I though 126-39-23.5 but there's a little gap between the circle, do you see?

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Actually...gap next to big circle too! :-\
 

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yea I see it but it dose not affect the solution. "c" is the intersection between the tangent and the horizontal line "rs". and "ra " is perpendicular to the tangent it is a theorem the angle $acr = y$ I used sine definition to come up with $\sin y = \frac{23.5}{rc} \rightarrow rc = \frac{23.5}{\sin y}$
 
  • #10
Hi megani,

Welcome to MHB! This appears to be part of a graded assignment. If so, are you allowed to receive outside help? I ask only to confirm that we aren't taking part in unallowed assistance.
 
  • #11
Jameson said:
Hi megani,

Welcome to MHB! This appears to be part of a graded assignment. If so, are you allowed to receive outside help? I ask only to confirm that we aren't taking part in unallowed assistance.

Hi. No. I'm actually a learning support teacher (main focus numeracy) and my colleague and I are developing a revision workbook for some Dip. Engineering students and this was one of their resources.
 

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