Mixing
Algorithm for converting a coordinate into angles of a pentagon.
$begingroup$
I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything.
I have a pentagon, and I know two top points (A & B) and the distance between them (black). I also know the other 4 side lengths (blue), which are all the same. I know the bottom point too, and I don't care about the two side points.
How can I use the bottom point (E) to determine the angle between each of the top two points, and their adjacent side lengths?
EDIT:
Points A, B, & E are known.
All side lengths are known.
Side lengths of the same colour are equal.
Angles that I want to know have dotted lines.
EDIT II: I realize my question may need clarification. The pentagon is on a coordinate plane. I know the location of A, B, and E. I want to use point E to find the interior angles on points A & B.
geometry polygons angle
edited Jan 26 at 14:58
Aretino
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
$endgroup$
add a comment |
$begingroup$
I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything.
I have a pentagon, and I know two top points (A & B) and the distance between them (black). I also know the other 4 side lengths (blue), which are all the same. I know the bottom point too, and I don't care about the two side points.
How can I use the bottom point (E) to determine the angle between each of the top two points, and their adjacent side lengths?
EDIT:
Points A, B, & E are known.
All side lengths are known.
Side lengths of the same colour are equal.
Angles that I want to know have dotted lines.
EDIT II: I realize my question may need clarification. The pentagon is on a coordinate plane. I know the location of A, B, and E. I want to use point E to find the interior angles on points A & B.
geometry polygons angle
edited Jan 26 at 14:58
Aretino
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
$endgroup$
$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52
add a comment |
$begingroup$
I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything.
I have a pentagon, and I know two top points (A & B) and the distance between them (black). I also know the other 4 side lengths (blue), which are all the same. I know the bottom point too, and I don't care about the two side points.
How can I use the bottom point (E) to determine the angle between each of the top two points, and their adjacent side lengths?
EDIT:
Points A, B, & E are known.
All side lengths are known.
Side lengths of the same colour are equal.
Angles that I want to know have dotted lines.
EDIT II: I realize my question may need clarification. The pentagon is on a coordinate plane. I know the location of A, B, and E. I want to use point E to find the interior angles on points A & B.
geometry polygons angle
edited Jan 26 at 14:58
Aretino
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
$endgroup$
I will go ahead and admit, this might just be something obvious but I did research and couldn't find anything.
I have a pentagon, and I know two top points (A & B) and the distance between them (black). I also know the other 4 side lengths (blue), which are all the same. I know the bottom point too, and I don't care about the two side points.
How can I use the bottom point (E) to determine the angle between each of the top two points, and their adjacent side lengths?
EDIT:
Points A, B, & E are known.
All side lengths are known.
Side lengths of the same colour are equal.
Angles that I want to know have dotted lines.
EDIT II: I realize my question may need clarification. The pentagon is on a coordinate plane. I know the location of A, B, and E. I want to use point E to find the interior angles on points A & B.
geometry polygons angle
geometry polygons angle
edited Jan 26 at 14:58
Aretino
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
edited Jan 26 at 14:58
Aretino
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
edited Jan 26 at 14:58
Aretino
25.4k21445
edited Jan 26 at 14:58
Aretino
25.4k21445
edited Jan 26 at 14:58
Aretino
25.4k21445
25.4k21445
asked Jan 26 at 13:17
12buntu12buntu
11
asked Jan 26 at 13:17
12buntu12buntu
11
asked Jan 26 at 13:17
12buntu12buntu
11
11
$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52
add a comment |
$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52
$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You want to find angle $alpha+beta$ in diagram below, and the analogous angle of vertex $B$ (caution: names of points are different from those in the question). By standard trigonometry we have:
$$
cosalpha={AHover AD}={{1over2}ACover AD},
quad
cosbeta={AB^2+AC^2-BC^2over2,ABcdot AC}.
$$
And similar formulas for the angles of vertex $B$.
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
$endgroup$
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You want to find angle $alpha+beta$ in diagram below, and the analogous angle of vertex $B$ (caution: names of points are different from those in the question). By standard trigonometry we have:
$$
cosalpha={AHover AD}={{1over2}ACover AD},
quad
cosbeta={AB^2+AC^2-BC^2over2,ABcdot AC}.
$$
And similar formulas for the angles of vertex $B$.
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
$endgroup$
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
add a comment |
$begingroup$
You want to find angle $alpha+beta$ in diagram below, and the analogous angle of vertex $B$ (caution: names of points are different from those in the question). By standard trigonometry we have:
$$
cosalpha={AHover AD}={{1over2}ACover AD},
quad
cosbeta={AB^2+AC^2-BC^2over2,ABcdot AC}.
$$
And similar formulas for the angles of vertex $B$.
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
$endgroup$
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
add a comment |
$begingroup$
You want to find angle $alpha+beta$ in diagram below, and the analogous angle of vertex $B$ (caution: names of points are different from those in the question). By standard trigonometry we have:
$$
cosalpha={AHover AD}={{1over2}ACover AD},
quad
cosbeta={AB^2+AC^2-BC^2over2,ABcdot AC}.
$$
And similar formulas for the angles of vertex $B$.
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
$endgroup$
You want to find angle $alpha+beta$ in diagram below, and the analogous angle of vertex $B$ (caution: names of points are different from those in the question). By standard trigonometry we have:
$$
cosalpha={AHover AD}={{1over2}ACover AD},
quad
cosbeta={AB^2+AC^2-BC^2over2,ABcdot AC}.
$$
And similar formulas for the angles of vertex $B$.
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
edited Jan 27 at 11:53
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
answered Jan 26 at 14:30
AretinoAretino
25.4k21445
25.4k21445
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
add a comment |
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
Sorry that my question wasn't clear. I have since edited it and included a picture for clarification.
$endgroup$
– 12buntu
Jan 26 at 14:44
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
$begingroup$
My solution works fine even if $AB$ is different from the other sides.
$endgroup$
– Aretino
Jan 26 at 14:55
add a comment |
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$begingroup$
It’s difficult to see exactly what you’re asking, could you draw a picture labeled with the information you know and the angle you would like to determine?
$endgroup$
– Alex
Jan 26 at 13:28
$begingroup$
@Alex Thank you. I have added a picture and some clarification
$endgroup$
– 12buntu
Jan 26 at 14:52