Length of a segment intersecting a square [closed]
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I have the following schema and I need to find the lengths of the colored segments.
From some calculations and help, I discovered that it should be something like
$$LB = Lleft(frac{1}{cos 45^circ} - frac{1}{2cos^2 45^circ}right)$$
$$LR = frac{L}{2cos^2 45^circ}$$
($L$ is the distance between points.)
But can that be generalized to other lengths and angles? What is the mathematics behind it?
geometry trigonometry
edited Nov 16 at 11:29
Blue
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
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Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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closed as unclear what you're asking by Jens, Paul Frost, Trevor Gunn, John B, Gibbs Nov 16 at 23:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-1
down vote
favorite
I have the following schema and I need to find the lengths of the colored segments.
From some calculations and help, I discovered that it should be something like
$$LB = Lleft(frac{1}{cos 45^circ} - frac{1}{2cos^2 45^circ}right)$$
$$LR = frac{L}{2cos^2 45^circ}$$
($L$ is the distance between points.)
But can that be generalized to other lengths and angles? What is the mathematics behind it?
geometry trigonometry
edited Nov 16 at 11:29
Blue
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as unclear what you're asking by Jens, Paul Frost, Trevor Gunn, John B, Gibbs Nov 16 at 23:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I have the following schema and I need to find the lengths of the colored segments.
From some calculations and help, I discovered that it should be something like
$$LB = Lleft(frac{1}{cos 45^circ} - frac{1}{2cos^2 45^circ}right)$$
$$LR = frac{L}{2cos^2 45^circ}$$
($L$ is the distance between points.)
But can that be generalized to other lengths and angles? What is the mathematics behind it?
geometry trigonometry
edited Nov 16 at 11:29
Blue
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have the following schema and I need to find the lengths of the colored segments.
From some calculations and help, I discovered that it should be something like
$$LB = Lleft(frac{1}{cos 45^circ} - frac{1}{2cos^2 45^circ}right)$$
$$LR = frac{L}{2cos^2 45^circ}$$
($L$ is the distance between points.)
But can that be generalized to other lengths and angles? What is the mathematics behind it?
geometry trigonometry
geometry trigonometry
edited Nov 16 at 11:29
Blue
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 16 at 11:29
Blue
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 16 at 11:29
Blue
46.3k869146
edited Nov 16 at 11:29
Blue
46.3k869146
edited Nov 16 at 11:29
Blue
46.3k869146
46.3k869146
asked Nov 16 at 9:35
Naeriel
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 16 at 9:35
Naeriel
22
asked Nov 16 at 9:35
Naeriel
22
22
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Naeriel is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as unclear what you're asking by Jens, Paul Frost, Trevor Gunn, John B, Gibbs Nov 16 at 23:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Jens, Paul Frost, Trevor Gunn, John B, Gibbs Nov 16 at 23:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08
add a comment |
What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08
What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08
What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08
add a comment |
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What is LB and LR? $P_4$ appears to lie on the line with the colored segments, but what are the coordinates of $P_4$? And what is the purpose of the other points $P_i$?
– Jens
Nov 16 at 15:08