How can I find the radius of this circle. Versine, x, and theta are known. (diagram included)

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diagram



So we know the versine length, and we know the length of x (blue line). We also know the angle theta. From this information it is simple to find the lengths of the dotted blue/green line (idk if we need that info or not). How can I find the radius of this circle? I am pretty sure that I can find the radius if I can find L, so maybe that is a necessary intermediate step.



Thank you in advance.




trigonometry circle




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  • Try to not link in diagrams
    – Rushabh Mehta
    Aug 1 at 14:28










  • Is it possible to embed diagrams?
    – it10101
    Aug 1 at 14:44










  • Yes, import pictures
    – Rushabh Mehta
    Aug 1 at 14:45














up vote
-1
down vote

favorite












diagram



So we know the versine length, and we know the length of x (blue line). We also know the angle theta. From this information it is simple to find the lengths of the dotted blue/green line (idk if we need that info or not). How can I find the radius of this circle? I am pretty sure that I can find the radius if I can find L, so maybe that is a necessary intermediate step.



Thank you in advance.




trigonometry circle




share|cite|improve this question



















  • Try to not link in diagrams
    – Rushabh Mehta
    Aug 1 at 14:28










  • Is it possible to embed diagrams?
    – it10101
    Aug 1 at 14:44










  • Yes, import pictures
    – Rushabh Mehta
    Aug 1 at 14:45












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











diagram



So we know the versine length, and we know the length of x (blue line). We also know the angle theta. From this information it is simple to find the lengths of the dotted blue/green line (idk if we need that info or not). How can I find the radius of this circle? I am pretty sure that I can find the radius if I can find L, so maybe that is a necessary intermediate step.



Thank you in advance.




trigonometry circle




share|cite|improve this question











diagram



So we know the versine length, and we know the length of x (blue line). We also know the angle theta. From this information it is simple to find the lengths of the dotted blue/green line (idk if we need that info or not). How can I find the radius of this circle? I am pretty sure that I can find the radius if I can find L, so maybe that is a necessary intermediate step.



Thank you in advance.





trigonometry circle





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 1 at 13:55









it10101

31




31











  • Try to not link in diagrams
    – Rushabh Mehta
    Aug 1 at 14:28










  • Is it possible to embed diagrams?
    – it10101
    Aug 1 at 14:44










  • Yes, import pictures
    – Rushabh Mehta
    Aug 1 at 14:45
















  • Try to not link in diagrams
    – Rushabh Mehta
    Aug 1 at 14:28










  • Is it possible to embed diagrams?
    – it10101
    Aug 1 at 14:44










  • Yes, import pictures
    – Rushabh Mehta
    Aug 1 at 14:45















Try to not link in diagrams
– Rushabh Mehta
Aug 1 at 14:28




Try to not link in diagrams
– Rushabh Mehta
Aug 1 at 14:28












Is it possible to embed diagrams?
– it10101
Aug 1 at 14:44




Is it possible to embed diagrams?
– it10101
Aug 1 at 14:44












Yes, import pictures
– Rushabh Mehta
Aug 1 at 14:45




Yes, import pictures
– Rushabh Mehta
Aug 1 at 14:45










2 Answers
2






active

oldest

votes

















up vote
1
down vote



accepted










Lets $v$ be versine, and $R$ be the radius.



By the law of cosines.



$R^2 = (R-v)^2 + x^2 + 2(R-v)xcostheta$



And solve for $R$



$R = frac v^2 + x^2 - 2vxcostheta2v-2xcostheta$






share|cite|improve this answer





















  • This seems to work! Thank you, Doug.
    – it10101
    Aug 1 at 14:45

















up vote
0
down vote













By Law of Cosines, $R^2 = x^2 + (R-v)^2 + 2x(R-v)costheta$.



Solving this should give your solution.






share|cite|improve this answer























  • Oops, my bad, I'll fix that
    – Rushabh Mehta
    Aug 1 at 14:45










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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










Lets $v$ be versine, and $R$ be the radius.



By the law of cosines.



$R^2 = (R-v)^2 + x^2 + 2(R-v)xcostheta$



And solve for $R$



$R = frac v^2 + x^2 - 2vxcostheta2v-2xcostheta$






share|cite|improve this answer





















  • This seems to work! Thank you, Doug.
    – it10101
    Aug 1 at 14:45














up vote
1
down vote



accepted










Lets $v$ be versine, and $R$ be the radius.



By the law of cosines.



$R^2 = (R-v)^2 + x^2 + 2(R-v)xcostheta$



And solve for $R$



$R = frac v^2 + x^2 - 2vxcostheta2v-2xcostheta$






share|cite|improve this answer





















  • This seems to work! Thank you, Doug.
    – it10101
    Aug 1 at 14:45












up vote
1
down vote



accepted







up vote
1
down vote



accepted






Lets $v$ be versine, and $R$ be the radius.



By the law of cosines.



$R^2 = (R-v)^2 + x^2 + 2(R-v)xcostheta$



And solve for $R$



$R = frac v^2 + x^2 - 2vxcostheta2v-2xcostheta$






share|cite|improve this answer













Lets $v$ be versine, and $R$ be the radius.



By the law of cosines.



$R^2 = (R-v)^2 + x^2 + 2(R-v)xcostheta$



And solve for $R$



$R = frac v^2 + x^2 - 2vxcostheta2v-2xcostheta$







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 1 at 14:37









Doug M

39k31749




39k31749











  • This seems to work! Thank you, Doug.
    – it10101
    Aug 1 at 14:45
















  • This seems to work! Thank you, Doug.
    – it10101
    Aug 1 at 14:45















This seems to work! Thank you, Doug.
– it10101
Aug 1 at 14:45




This seems to work! Thank you, Doug.
– it10101
Aug 1 at 14:45










up vote
0
down vote













By Law of Cosines, $R^2 = x^2 + (R-v)^2 + 2x(R-v)costheta$.



Solving this should give your solution.






share|cite|improve this answer























  • Oops, my bad, I'll fix that
    – Rushabh Mehta
    Aug 1 at 14:45














up vote
0
down vote













By Law of Cosines, $R^2 = x^2 + (R-v)^2 + 2x(R-v)costheta$.



Solving this should give your solution.






share|cite|improve this answer























  • Oops, my bad, I'll fix that
    – Rushabh Mehta
    Aug 1 at 14:45












up vote
0
down vote










up vote
0
down vote









By Law of Cosines, $R^2 = x^2 + (R-v)^2 + 2x(R-v)costheta$.



Solving this should give your solution.






share|cite|improve this answer















By Law of Cosines, $R^2 = x^2 + (R-v)^2 + 2x(R-v)costheta$.



Solving this should give your solution.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 1 at 14:45


























answered Aug 1 at 14:39









Rushabh Mehta

411110




411110











  • Oops, my bad, I'll fix that
    – Rushabh Mehta
    Aug 1 at 14:45
















  • Oops, my bad, I'll fix that
    – Rushabh Mehta
    Aug 1 at 14:45















Oops, my bad, I'll fix that
– Rushabh Mehta
Aug 1 at 14:45




Oops, my bad, I'll fix that
– Rushabh Mehta
Aug 1 at 14:45












 

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