^j"~dZddlmZmZddlmZmZmZmZm Z m Z m Z edz Z dZ dZdZdZdd Zd Zd Zd ZdZy )a{ Written by Steven Byrnes, http://sjbyrnes.com/ Download: https://pypi.python.org/pypi/trianglesolver/ Source code repository: https://github.com/sbyrnes321/trianglesolver This little package applies the law of sines or cosines to find all the sides and angles of a triangle, if you know some of the sides and/or angles. The main function defined by this package is solve(...). Simple example:: from math import pi from trianglesolver import solve a,b,c,A,B,C = solve(b=7.6, c=8.3, A=pi/3) Following the usual convention, lower-case letters are side lengths and capital letters are angles. Corresponding letters are opposite each other, e.g. side b is opposite angle B. All angles are in radians! However, you can use the degree constant to convert:: from trianglesolver import solve, degree a,b,c,A,B,C = solve(b=7, A=5*degree, B=70*degree) print(C / degree) )divisionprint_function)sincospisqrtacosasinisclosecz|t|zt|z }|t|zt|z }||||||fS)= This function solves the triangle and returns (d,e,f,D,E,F) )r)DEFfdes G/opt/ringagent/.cad-venv/lib/python3.12/site-packages/trianglesolver.pyaaasr&s@ CF SVA CF SVA a!Aa=c||z|kDr||z|kDr||z|kDsJt|dz|dzz|dzz d|z|zz }t|dz|dzz|dzz d|z|zz }t|z |z }||||||fSr)r r)rrrrrrs rsssr,s q519Qq1uqy0 0 adQTkAqD QUQY /0A adQTkAqD QUQY /0A Q A a!Aa=rcnt|dz|dzzd|z|zt|zz }t|||Sr)rrr)rrrrs rsasr4s< QTAqD[1q519s1v- -.A q1:rc |dvsJdt||z|z }t|dr tdz }n|dksJdt|}t|z }dt|z |z cxkxr tknc}dt|z |z cxkxr tknc} |dk(r |sJd|}n<|dk(r | sJd|}n+|d k(sJ|r | r t d |s | s t d|r|n|}t|z |z } t || ||\}} }}} }||| ||| fS) zu This function solves the triangle and returns (d,e,f,D,E,F) See docstring for solve() for definition of ssa_flag)acuteobtuseforbidzInvalid value of ssa_flagrzNo such trianglerrr r!z,Two different triangles fit this description)rr rr ValueErrorr) rrrssa_flagsinErE_acuteE_obtuseacute_is_validobtuse_is_validrrs rssar*:s< 4 4Q6QQ 4 q6A:>DtQ qDax+++xt*<rAv/525Q 17R7 w ! 5#5 5>A  !" 6$6 6?Ax' ''/ !OPP"_ !344)xA Q Aq1Q-KAa!Aa a!Aa=rNc td||||||fDdk7r tdtd|||fDdk(r tdtd||||||fDsJtd|||fDsJ|dvsJtd |||fDdk(rt|||\}}}}}}||||||fStd |||fDd k(rtd |||fDrt ||||\}}}}}}nbtd |||fDrt ||||\}}}}}}n6td|||fDrt ||||\}}}}}}n td|||fDrt ||||\}}}}}}ntd|||fDrt ||||\}}}}}}ntd|||fDrt ||||\}}}}}}ntd|||fDrt |||\}}}}}}n_td|||fDrt |||\}}}}}}n5td|||fDrt |||\}}}}}}n td||||||fStd|||fDdk(r| t |z |z }n| t |z |z }n t |z |z }|dkDr |dkDr|dkDsJ|t||||\}}}}}}n-|t||||\}}}}}}nt||||\}}}}}}||||||fStd)u! Solve to find all the information about a triangle, given partial information. a, b, c, A, B, and C are the three sides and angles. (e.g. A is the angle opposite the side of length a.) Out of these six possibilities, you need to tell the program exactly three. Then the program will tell you all six. It returns a tuple (a, b, c, A, B, C). "ssa" is the situation when you give two sides and an angle which is not between them. This is usually not enough information to specify a unique triangle. Usually there are two possible triangles—except for a special case with right triangles where the two possible triangles are the same (the equation has a "double root"), and some cases where one of the two possible triangles has a negative angle. Therefore there is an 'ssa_flag'. You can set it to'forbid' (raise an error if the answer is not unique - the default setting), or 'acute' (where the unknown angle across from the known side is chosen to be acute) or 'obtuse' (similarly). c3$K|]}|du ywN.0xs r zsolve..ws 0Q1D= 0zMust provide exactly 3 inputsc3$K|]}|du ywr-r.r/s rr2zsolve..ys &19 &r3z#Must provide at least 1 side lengthc3,K|] }||dkDyw)Nrr.r/s rr2zsolve..{s=q}q1u=s c34K|]}||tkywr-)rr/s rr2zsolve..|s8!!-q2v8s)r!rr c3$K|]}|du ywr-r.r/s rr2zsolve.. *Q1D= *r3c3$K|]}|du ywr-r.r/s rr2zsolve..r9r3rc3$K|]}|du ywr-r.r/s rr2zsolve..s0q}0r3c3$K|]}|du ywr-r.r/s rr2zsolve..21$2r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3c3$K|]}|du ywr-r.r/s rr2zsolve..r=r3z Oops, this code should never runc3$K|]}|du ywr-r.r/s rr2zsolve..r9r3r"r)sumr#allrr*rrr)abcABCr$s rsolverN`s. 01Qq1Q- 00A5899 &q1g &&!+>?? =q1Qqm= == = 8!Aw8 88 8 4 44 4 *1Qq' **a/!Aaj !Aa!!Aa!} *1Qq' **a/ 0q!Qi0 0aAx0KAa!Aa 2Aq 2 2aAx0KAa!Aa 2Aq 2 2aAx0KAa!Aa 2Aq 2 2aAx0KAa!Aa 2Aq 2 2aAx0KAa!Aa 2Aq 2 2aAx0KAa!Aa2Aq 2 2aA,KAa!Aa 2Aq 2 2aA,KAa!Aa 2Aq 2 2aA,KAa!Aa?@ @!Aa!} *1Qq' **a/ 9Q A YQ AQ A1uQ1q5(( =q1Q-KAa!Aa ]q1Q-KAa!Aaq1Q-KAa!Aa!Aa!} 7 88rcTtfdttDS)Nc3BK|]}t||ywr-)r )r0ir1ys rr2z tuple_isclose..s :qwqtQqT":s)rGrangelen)r1rRs``r tuple_iscloserUs :E#a&M: ::rct|t|z |t|z sJt|t|z |t|z sJt|dz|dz|dzzd|z|zt|zz sJt|dz|dz|dzzd|z|zt|zz sJt|dz|dz|dzzd|z|zt|zz sJy)zJ Check that the triangle satisfies the law of cosines and law of sinesrN)r rr)rHrIrJrKrLrMs r test_trianglerWs 1SV8Qs1vX && & 1SV8Qs1vX && & 1a4A1q1uqy3q6'99 :: : 1a4A1q1uqy3q6'99 :: : 1a4A1q1uqy3q6'99 :: :rc t|||\}}}}}}t|||f|||fsJt||||||||||||f} t| t|||sJt| t|||sJt| t|||sJt| t|||sJt| t|||sJt| t|||sJt| t|||sJt| t||| sJt| t||| sJt| t||| sJt| t||| sJt| t||| sJ|tdz krdnd} |tdz krdnd} |tdz krdnd} t| t|||| sJt| t|||| sJt| t|||| sJt| t|||| sJt| t|||| sJt| t|||| sJy)z< Test that the program works, for a triangle of sides a,b,c.rHrIrJ)rHrIrM)rHrJrL)rIrJrK)rHrKrL)rHrKrM)rHrLrM)rIrKrL)rIrKrM)rIrLrM)rJrKrL)rJrKrM)rJrLrMrrr )rHrIrKr$)rHrIrLr$)rHrJrKr$)rHrJrMr$)rIrJrLr$)rIrJrMr$N)rNrUrWr) rHrIrJa1b1c1rKrLrMtriAtypeBtypeCtypes r test_solverrasdQQ'NBr"Qq !Aa2b* -- -!Aa!A Qq1Q-C ea!a0 11 1 ea!a0 11 1 ea!a0 11 1 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 3 ea12 33 32a4xGXE2a4xGXE2a4xGXE ea1EB CC C ea1EB CC C ea1EB CC C ea1EB CC C ea1EB CC C ea1EB CC CrcJdD]\}}}t|||tdy)N)) ) )rfrhrg)rhrfrg)rf )rirfrj)rirjrfzAll tests pass!)raprintrYs rrun_lots_of_testsrls0(!AAa r)NNNNNNr!)__doc__ __future__rrmathrrrrr r r degreerrrr*rNrUrWrarlr.rrrqsU80888 C  !LQ9n;;"DHr