How can people assume this angle is exactly half of the other angle?
Long story short what I don't understand is underlined here in red:
So, they somehow seem to assume the angle on the triangle on the right has an angle $frac{theta}{2}$.
How do they know that? How can they assume it is exactly half of the angle of theta?
Thanks
EDIT: to give a bit more of a context, it has to do with the mapping of a rocket's position in the ground-fixed coordinates to the spherical earth's coordinates. When going from one coordinate to the other the altitude varies.
geometry
asked 2 days ago
traduceradtraducerad
1184
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traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
Long story short what I don't understand is underlined here in red:
So, they somehow seem to assume the angle on the triangle on the right has an angle $frac{theta}{2}$.
How do they know that? How can they assume it is exactly half of the angle of theta?
Thanks
EDIT: to give a bit more of a context, it has to do with the mapping of a rocket's position in the ground-fixed coordinates to the spherical earth's coordinates. When going from one coordinate to the other the altitude varies.
geometry
asked 2 days ago
traduceradtraducerad
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How was the triangle on the left constructed?
– Mike
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago
add a comment |
Long story short what I don't understand is underlined here in red:
So, they somehow seem to assume the angle on the triangle on the right has an angle $frac{theta}{2}$.
How do they know that? How can they assume it is exactly half of the angle of theta?
Thanks
EDIT: to give a bit more of a context, it has to do with the mapping of a rocket's position in the ground-fixed coordinates to the spherical earth's coordinates. When going from one coordinate to the other the altitude varies.
geometry
asked 2 days ago
traduceradtraducerad
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Long story short what I don't understand is underlined here in red:
So, they somehow seem to assume the angle on the triangle on the right has an angle $frac{theta}{2}$.
How do they know that? How can they assume it is exactly half of the angle of theta?
Thanks
EDIT: to give a bit more of a context, it has to do with the mapping of a rocket's position in the ground-fixed coordinates to the spherical earth's coordinates. When going from one coordinate to the other the altitude varies.
geometry
geometry
asked 2 days ago
traduceradtraducerad
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
traduceradtraducerad
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
traducerad
asked 2 days ago
traduceradtraducerad
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
traduceradtraducerad
1184
asked 2 days ago
traduceradtraducerad
1184
1184
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
traducerad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How was the triangle on the left constructed?
– Mike
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago
add a comment |
How was the triangle on the left constructed?
– Mike
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago
How was the triangle on the left constructed?
– Mike
2 days ago
How was the triangle on the left constructed?
– Mike
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago
add a comment |
1 Answer
1
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There is an isoscales triangle between the circle center $C$ and the 2 points $A$ and $B$ where the lines through the center meet the circle. The angle at $C$ is $theta$, so each base angle is $90^circ-fractheta2 = angle CAB$. Since the tangent has a right angle with the radius ($angle CAD=90^circ$), the angle under consideration ($angle BAD)$ is $fractheta2$.
answered 2 days ago
IngixIngix
3,344145
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
Great question @traducerad btw!
– Mike
2 days ago
|
show 2 more comments
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
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votes
active
oldest
votes
There is an isoscales triangle between the circle center $C$ and the 2 points $A$ and $B$ where the lines through the center meet the circle. The angle at $C$ is $theta$, so each base angle is $90^circ-fractheta2 = angle CAB$. Since the tangent has a right angle with the radius ($angle CAD=90^circ$), the angle under consideration ($angle BAD)$ is $fractheta2$.
answered 2 days ago
IngixIngix
3,344145
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
Great question @traducerad btw!
– Mike
2 days ago
|
show 2 more comments
There is an isoscales triangle between the circle center $C$ and the 2 points $A$ and $B$ where the lines through the center meet the circle. The angle at $C$ is $theta$, so each base angle is $90^circ-fractheta2 = angle CAB$. Since the tangent has a right angle with the radius ($angle CAD=90^circ$), the angle under consideration ($angle BAD)$ is $fractheta2$.
answered 2 days ago
IngixIngix
3,344145
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
Great question @traducerad btw!
– Mike
2 days ago
|
show 2 more comments
There is an isoscales triangle between the circle center $C$ and the 2 points $A$ and $B$ where the lines through the center meet the circle. The angle at $C$ is $theta$, so each base angle is $90^circ-fractheta2 = angle CAB$. Since the tangent has a right angle with the radius ($angle CAD=90^circ$), the angle under consideration ($angle BAD)$ is $fractheta2$.
answered 2 days ago
IngixIngix
3,344145
There is an isoscales triangle between the circle center $C$ and the 2 points $A$ and $B$ where the lines through the center meet the circle. The angle at $C$ is $theta$, so each base angle is $90^circ-fractheta2 = angle CAB$. Since the tangent has a right angle with the radius ($angle CAD=90^circ$), the angle under consideration ($angle BAD)$ is $fractheta2$.
answered 2 days ago
IngixIngix
3,344145
edited 2 days ago
answered 2 days ago
IngixIngix
3,344145
answered 2 days ago
IngixIngix
3,344145
answered 2 days ago
IngixIngix
3,344145
3,344145
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
Great question @traducerad btw!
– Mike
2 days ago
|
show 2 more comments
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
Great question @traducerad btw!
– Mike
2 days ago
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
If you could provide a small ugly drawing to clarify what you mean, I'll accept your answer
– traducerad
2 days ago
1
1
@traducerad Added the picture
– Ingix
2 days ago
@traducerad Added the picture
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
@ThomasShelby You think the assumption that (in my notation) $CA$ is a radius and $AD$ a tangent is strange?
– Ingix
2 days ago
Great answer @Ingix
– Mike
2 days ago
Great answer @Ingix
– Mike
2 days ago
1
1
Great question @traducerad btw!
– Mike
2 days ago
Great question @traducerad btw!
– Mike
2 days ago
|
show 2 more comments
traducerad is a new contributor. Be nice, and check out our Code of Conduct.
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traducerad is a new contributor. Be nice, and check out our Code of Conduct.
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How was the triangle on the left constructed?
– Mike
2 days ago
Is this something related to physics?
– Thomas Shelby
2 days ago
@ThomasShelby yes this is related to physics
– traducerad
2 days ago