Mixing
A trigonometry problem for a graphic designer (includes graphic)
$begingroup$
I am in no way a mathematician, I am a graphic designer by trade but I do like precision in what I do.
Quite a tricky one to describe hence the attached graphic, however, in words;
I have punched a circle out of a square of the same dimensions. I have discarded all but the top left corner shape. I'd now like to round this corner off. So at 30 degrees from the top right I have created a point, from this point I'd like to draw a circle (green) until it fills the available space.
I therefore want to calculate the radius of the green circle. But my limited maths knowledge means I'm struggling and would be very grateful for any help.
I have the angles a, b and c. I also have the lengths of d, e and f.
trigonometry
edited Jan 31 at 17:59
Blue
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
$endgroup$
add a comment |
$begingroup$
I am in no way a mathematician, I am a graphic designer by trade but I do like precision in what I do.
Quite a tricky one to describe hence the attached graphic, however, in words;
I have punched a circle out of a square of the same dimensions. I have discarded all but the top left corner shape. I'd now like to round this corner off. So at 30 degrees from the top right I have created a point, from this point I'd like to draw a circle (green) until it fills the available space.
I therefore want to calculate the radius of the green circle. But my limited maths knowledge means I'm struggling and would be very grateful for any help.
I have the angles a, b and c. I also have the lengths of d, e and f.
trigonometry
edited Jan 31 at 17:59
Blue
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
$endgroup$
add a comment |
$begingroup$
I am in no way a mathematician, I am a graphic designer by trade but I do like precision in what I do.
Quite a tricky one to describe hence the attached graphic, however, in words;
I have punched a circle out of a square of the same dimensions. I have discarded all but the top left corner shape. I'd now like to round this corner off. So at 30 degrees from the top right I have created a point, from this point I'd like to draw a circle (green) until it fills the available space.
I therefore want to calculate the radius of the green circle. But my limited maths knowledge means I'm struggling and would be very grateful for any help.
I have the angles a, b and c. I also have the lengths of d, e and f.
trigonometry
edited Jan 31 at 17:59
Blue
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
$endgroup$
I am in no way a mathematician, I am a graphic designer by trade but I do like precision in what I do.
Quite a tricky one to describe hence the attached graphic, however, in words;
I have punched a circle out of a square of the same dimensions. I have discarded all but the top left corner shape. I'd now like to round this corner off. So at 30 degrees from the top right I have created a point, from this point I'd like to draw a circle (green) until it fills the available space.
I therefore want to calculate the radius of the green circle. But my limited maths knowledge means I'm struggling and would be very grateful for any help.
I have the angles a, b and c. I also have the lengths of d, e and f.
trigonometry
trigonometry
edited Jan 31 at 17:59
Blue
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
edited Jan 31 at 17:59
Blue
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
edited Jan 31 at 17:59
Blue
49.5k870157
edited Jan 31 at 17:59
Blue
49.5k870157
edited Jan 31 at 17:59
Blue
49.5k870157
49.5k870157
asked Jan 31 at 17:03
morgyfacemorgyface
82
asked Jan 31 at 17:03
morgyfacemorgyface
82
asked Jan 31 at 17:03
morgyfacemorgyface
82
82
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If radius of green circle is $r$, then for length $OD$:
$$
OD = OB+BC+CD,\
frac d{cos a} = d + r + frac r{cos a},\
rleft(frac 1{cos a}+1right) = dleft(frac 1{cos a}-1right)
r = dfrac{1-cos a}{1+cos a}
$$
If $a=30°$, then $r = (7-4sqrt 3)d approx 0.0718 d$.
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
$endgroup$
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3095157%2fa-trigonometry-problem-for-a-graphic-designer-includes-graphic%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If radius of green circle is $r$, then for length $OD$:
$$
OD = OB+BC+CD,\
frac d{cos a} = d + r + frac r{cos a},\
rleft(frac 1{cos a}+1right) = dleft(frac 1{cos a}-1right)
r = dfrac{1-cos a}{1+cos a}
$$
If $a=30°$, then $r = (7-4sqrt 3)d approx 0.0718 d$.
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
$endgroup$
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
add a comment |
$begingroup$
If radius of green circle is $r$, then for length $OD$:
$$
OD = OB+BC+CD,\
frac d{cos a} = d + r + frac r{cos a},\
rleft(frac 1{cos a}+1right) = dleft(frac 1{cos a}-1right)
r = dfrac{1-cos a}{1+cos a}
$$
If $a=30°$, then $r = (7-4sqrt 3)d approx 0.0718 d$.
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
$endgroup$
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
add a comment |
$begingroup$
If radius of green circle is $r$, then for length $OD$:
$$
OD = OB+BC+CD,\
frac d{cos a} = d + r + frac r{cos a},\
rleft(frac 1{cos a}+1right) = dleft(frac 1{cos a}-1right)
r = dfrac{1-cos a}{1+cos a}
$$
If $a=30°$, then $r = (7-4sqrt 3)d approx 0.0718 d$.
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
$endgroup$
If radius of green circle is $r$, then for length $OD$:
$$
OD = OB+BC+CD,\
frac d{cos a} = d + r + frac r{cos a},\
rleft(frac 1{cos a}+1right) = dleft(frac 1{cos a}-1right)
r = dfrac{1-cos a}{1+cos a}
$$
If $a=30°$, then $r = (7-4sqrt 3)d approx 0.0718 d$.
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
edited Jan 31 at 17:23
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
answered Jan 31 at 17:11
Vasily MitchVasily Mitch
2,6791312
2,6791312
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
add a comment |
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
This is mind blowing, I quickly finished off the design work after sizing the green circle correctly, and I'm now returning to try and get my head round the equation. I'm incredibly grateful for the help, thank you @vasily-mitch
$endgroup$
– morgyface
Jan 31 at 18:49
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
$begingroup$
Glad to help. You might refresh basic trigonometry in a right triangle and notice the similarity between small red triangle and big $OAD$
$endgroup$
– Vasily Mitch
Jan 31 at 18:57
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3095157%2fa-trigonometry-problem-for-a-graphic-designer-includes-graphic%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
