Looking for correlation between length and angle
up vote
1
down vote
favorite
The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like h in the graphic) the 90-degree lines are too long.
So all I need to know is how to calculate the difference (x) which occurs if the line is not rotated by angle alpha.
Variables I know: alpha and h
geometry angle
add a comment |
up vote
1
down vote
favorite
The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like h in the graphic) the 90-degree lines are too long.
So all I need to know is how to calculate the difference (x) which occurs if the line is not rotated by angle alpha.
Variables I know: alpha and h
geometry angle
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like h in the graphic) the 90-degree lines are too long.
So all I need to know is how to calculate the difference (x) which occurs if the line is not rotated by angle alpha.
Variables I know: alpha and h
geometry angle
The problem I'm facing might be rather easy to solve, but I can't think of a way how to do it atm. I want to clip straight 90-degree and some other degree lines. If I clip them at a fixed height (like h in the graphic) the 90-degree lines are too long.
So all I need to know is how to calculate the difference (x) which occurs if the line is not rotated by angle alpha.
Variables I know: alpha and h
geometry angle
geometry angle
asked Nov 22 at 16:25
Sector
254
254
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
The portion of the blue line segment between the vertex and the intersection with the dashed line must have length $x+h$, and that allows you to find $x$ like so:
$$begin{align}
cos(alpha)&=frac{h}{x+h} \[0.2ex]
x+h&=hsec(alpha) \[0.7ex]
x&=h(sec(alpha)-1)
end{align}$$
add a comment |
up vote
1
down vote
Use Cosine(x) = adjacent / hypotenuse
New contributor
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
The portion of the blue line segment between the vertex and the intersection with the dashed line must have length $x+h$, and that allows you to find $x$ like so:
$$begin{align}
cos(alpha)&=frac{h}{x+h} \[0.2ex]
x+h&=hsec(alpha) \[0.7ex]
x&=h(sec(alpha)-1)
end{align}$$
add a comment |
up vote
1
down vote
accepted
The portion of the blue line segment between the vertex and the intersection with the dashed line must have length $x+h$, and that allows you to find $x$ like so:
$$begin{align}
cos(alpha)&=frac{h}{x+h} \[0.2ex]
x+h&=hsec(alpha) \[0.7ex]
x&=h(sec(alpha)-1)
end{align}$$
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
The portion of the blue line segment between the vertex and the intersection with the dashed line must have length $x+h$, and that allows you to find $x$ like so:
$$begin{align}
cos(alpha)&=frac{h}{x+h} \[0.2ex]
x+h&=hsec(alpha) \[0.7ex]
x&=h(sec(alpha)-1)
end{align}$$
The portion of the blue line segment between the vertex and the intersection with the dashed line must have length $x+h$, and that allows you to find $x$ like so:
$$begin{align}
cos(alpha)&=frac{h}{x+h} \[0.2ex]
x+h&=hsec(alpha) \[0.7ex]
x&=h(sec(alpha)-1)
end{align}$$
answered Nov 22 at 16:48
Robert Howard
1,741722
1,741722
add a comment |
add a comment |
up vote
1
down vote
Use Cosine(x) = adjacent / hypotenuse
New contributor
add a comment |
up vote
1
down vote
Use Cosine(x) = adjacent / hypotenuse
New contributor
add a comment |
up vote
1
down vote
up vote
1
down vote
Use Cosine(x) = adjacent / hypotenuse
New contributor
Use Cosine(x) = adjacent / hypotenuse
New contributor
New contributor
answered Nov 22 at 16:28
John McGee
1361
1361
New contributor
New contributor
add a comment |
add a comment |
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%2f3009322%2flooking-for-correlation-between-length-and-angle%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