How can I find the length l on this cul de sac?
$begingroup$
I need to redraw this Cul de sac using autocad. I can do it if I know the value of l (which is the red l) but I cant think of how to obtain that value.
Also the angle of 55 degrees produces a length of 92.35. Can one use the proportion to find the angle that creates the 95.58 side?
Here is the cul de sac
geometry
$endgroup$
migrated from physics.stackexchange.com Feb 17 '14 at 8:49
This question came from our site for active researchers, academics and students of physics.
add a comment |
$begingroup$
I need to redraw this Cul de sac using autocad. I can do it if I know the value of l (which is the red l) but I cant think of how to obtain that value.
Also the angle of 55 degrees produces a length of 92.35. Can one use the proportion to find the angle that creates the 95.58 side?
Here is the cul de sac
geometry
$endgroup$
migrated from physics.stackexchange.com Feb 17 '14 at 8:49
This question came from our site for active researchers, academics and students of physics.
add a comment |
$begingroup$
I need to redraw this Cul de sac using autocad. I can do it if I know the value of l (which is the red l) but I cant think of how to obtain that value.
Also the angle of 55 degrees produces a length of 92.35. Can one use the proportion to find the angle that creates the 95.58 side?
Here is the cul de sac
geometry
$endgroup$
I need to redraw this Cul de sac using autocad. I can do it if I know the value of l (which is the red l) but I cant think of how to obtain that value.
Also the angle of 55 degrees produces a length of 92.35. Can one use the proportion to find the angle that creates the 95.58 side?
Here is the cul de sac
geometry
geometry
asked Feb 17 '14 at 3:55
Nik Brkic
migrated from physics.stackexchange.com Feb 17 '14 at 8:49
This question came from our site for active researchers, academics and students of physics.
migrated from physics.stackexchange.com Feb 17 '14 at 8:49
This question came from our site for active researchers, academics and students of physics.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
For the angle consider the right-angled triangle formed by a radius, the bisector of the angle and half the chord:
$$sin(a/2) = (c/2) / r$$
For finding $l$:
Let the point $C$ be the top point in the drawing, at the end of the first radius, and $D$ the other end of the length $l$ which you are looking for. Let $E$ be the foot of the perpendicular on $BD$ through $C$
BEC is a right angled triangle, you know the hypotenuse $BC$ and you can find the angle at $B$.
This lets you find the length of both $BE$ and $CE$.
Split the quadrilateral EDAC in a rectangle and a right angled triangle.
From the right angled triangle you know one (the vertical) leg and the hypotenuse. Determine the other leg, which has the same length as DE. The length $l$ you search is the total of $BE$ and $DE$.
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
$endgroup$
add a comment |
Your Answer
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%2f679279%2fhow-can-i-find-the-length-l-on-this-cul-de-sac%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
$begingroup$
For the angle consider the right-angled triangle formed by a radius, the bisector of the angle and half the chord:
$$sin(a/2) = (c/2) / r$$
For finding $l$:
Let the point $C$ be the top point in the drawing, at the end of the first radius, and $D$ the other end of the length $l$ which you are looking for. Let $E$ be the foot of the perpendicular on $BD$ through $C$
BEC is a right angled triangle, you know the hypotenuse $BC$ and you can find the angle at $B$.
This lets you find the length of both $BE$ and $CE$.
Split the quadrilateral EDAC in a rectangle and a right angled triangle.
From the right angled triangle you know one (the vertical) leg and the hypotenuse. Determine the other leg, which has the same length as DE. The length $l$ you search is the total of $BE$ and $DE$.
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
$endgroup$
add a comment |
$begingroup$
For the angle consider the right-angled triangle formed by a radius, the bisector of the angle and half the chord:
$$sin(a/2) = (c/2) / r$$
For finding $l$:
Let the point $C$ be the top point in the drawing, at the end of the first radius, and $D$ the other end of the length $l$ which you are looking for. Let $E$ be the foot of the perpendicular on $BD$ through $C$
BEC is a right angled triangle, you know the hypotenuse $BC$ and you can find the angle at $B$.
This lets you find the length of both $BE$ and $CE$.
Split the quadrilateral EDAC in a rectangle and a right angled triangle.
From the right angled triangle you know one (the vertical) leg and the hypotenuse. Determine the other leg, which has the same length as DE. The length $l$ you search is the total of $BE$ and $DE$.
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
$endgroup$
add a comment |
$begingroup$
For the angle consider the right-angled triangle formed by a radius, the bisector of the angle and half the chord:
$$sin(a/2) = (c/2) / r$$
For finding $l$:
Let the point $C$ be the top point in the drawing, at the end of the first radius, and $D$ the other end of the length $l$ which you are looking for. Let $E$ be the foot of the perpendicular on $BD$ through $C$
BEC is a right angled triangle, you know the hypotenuse $BC$ and you can find the angle at $B$.
This lets you find the length of both $BE$ and $CE$.
Split the quadrilateral EDAC in a rectangle and a right angled triangle.
From the right angled triangle you know one (the vertical) leg and the hypotenuse. Determine the other leg, which has the same length as DE. The length $l$ you search is the total of $BE$ and $DE$.
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
$endgroup$
For the angle consider the right-angled triangle formed by a radius, the bisector of the angle and half the chord:
$$sin(a/2) = (c/2) / r$$
For finding $l$:
Let the point $C$ be the top point in the drawing, at the end of the first radius, and $D$ the other end of the length $l$ which you are looking for. Let $E$ be the foot of the perpendicular on $BD$ through $C$
BEC is a right angled triangle, you know the hypotenuse $BC$ and you can find the angle at $B$.
This lets you find the length of both $BE$ and $CE$.
Split the quadrilateral EDAC in a rectangle and a right angled triangle.
From the right angled triangle you know one (the vertical) leg and the hypotenuse. Determine the other leg, which has the same length as DE. The length $l$ you search is the total of $BE$ and $DE$.
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
edited Feb 17 '14 at 9:16
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
answered Feb 17 '14 at 8:56
LeonhardLeonhard
1,499817
1,499817
add a comment |
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%2f679279%2fhow-can-i-find-the-length-l-on-this-cul-de-sac%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
