How can people assume this angle is exactly half of the other angle?












3














Long story short what I don't understand is underlined here in red:
enter image description here



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







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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
















3














Long story short what I don't understand is underlined here in red:
enter image description here



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







share|cite|improve this question









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














3












3








3







Long story short what I don't understand is underlined here in red:
enter image description here



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







share|cite|improve this question









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:
enter image description here



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






share|cite|improve this question









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.











share|cite|improve this question









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.









share|cite|improve this question




share|cite|improve this question








edited 2 days ago







traducerad













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asked 2 days ago









traduceradtraducerad

1184




1184




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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


















  • 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










1 Answer
1






active

oldest

votes


















4














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 $fractheta2$.



enter image description here






share|cite|improve this answer























  • 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











Your Answer





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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4














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 $fractheta2$.



enter image description here






share|cite|improve this answer























  • 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
















4














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 $fractheta2$.



enter image description here






share|cite|improve this answer























  • 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














4












4








4






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 $fractheta2$.



enter image description here






share|cite|improve this answer














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 $fractheta2$.



enter image description here







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago

























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


















  • 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










traducerad is a new contributor. Be nice, and check out our Code of Conduct.










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