<prompt> Ajay amesimama katika sehemu ya A karibu na Pontianak, Indonesia, 0circ latitudo na 110circ text E longitudo. Billy amesimama katika sehemu ya B karibu na Big Baldy Mountain, Idaho, Marekani, 45circ text N latitudo na 115circ text W longitudo. Chukulia kuwa Dunia ni duara kamili na katikati C. Je, kipimo cha shahada cha angle ACB ni kipi?  <response>: Acha B iwe sehemu ya 0circ latitudo na 115circ W longitudo. Tunaona kwamba angle ACB 360circ - 110circ - 115circ 135circ.asykuagiza tatu;kuagiza yabisi;ukubwa 200;makadirio ya sasa mtazamo 6,3,2;mara tatu A, B, Bp, C;A Cos110, Dhambi110,0;B Dhambi45Kos-115,Dhambi45Dhambi-115,Kos45;Bp Cos-115, Dhambi-115,0;C 0,0,0;kuchorausotufe1,kijivu0.9,nolight;chora1,0,0..Cos55,Sin55,0..Cos110,Sin110,0,nyekundu;chora1,0,0 ..Cos-1152,Sin-1152,0..Bp,nyekundu;choraBp..Dhambi45 902Cos-115,Dhambi45 902Dhambi-115,Cos45 902 ..B,nyekundu;chora-1.2,0,0--1.2,0,0,Arrow36;chora0,-1.2,0--0,1.2,0,Arrow36;chora0,0,-1.2--0,0,1.2,Arrow36;kuchoraC--A;kuchoraC--B;kuchoraC--Bp;lebox, 1.2,0,0, SW;leboy, 0,1.2,0, E;leboz, 0,0,1.2, N;lebo110circ, 0.3,0.2,0, nyekundu;lebo115circ, 0.3,-0.2,0, nyekundu;lebo45circ, -0.3,-0.5,0.1, nyekundu;nukta A, A, E;nuktaB, B, NW;nuktaB, Bp, NW;nukta C, C, NE;nukta 1,0,0;asyAcha D iwe nukta iliyo kinyume cha A, P iwe makadirio ya B kwenye yz-ndege, na Q iwe makadirio ya P kwenye mstari AD.asykuagiza tatu;kuagiza yabisi;ukubwa 200;makadirio ya sasa mtazamo 6,3,2;mara tatu A, B, Bp, C, D, P, Q;A Cos110, Dhambi110,0;B Dhambi45Kos-115,Dhambi45Dhambi-115,Kos45;Bp Cos-115, Dhambi-115,0;C 0,0,0;D -A;P B.x,B.y,0;Q D2;kuchorausotufe1,kijivu0.9,nolight;chora1,0,0..Cos55,Sin55,0..Cos110,Sin110,0,nyekundu;chora1,0,0 ..Cos-1152,Sin-1152,0..Bp,nyekundu;choraBp..Dhambi45 902Cos-115,Dhambi45 902Dhambi-115,Cos45 902 ..B,nyekundu;chora-1.2,0,0--1.2,0,0,Arrow36;chora0,-1.2,0--0,1.2,0,Arrow36;chora0,0,-1.2--0,0,1.2,Arrow36;kuchoraC--A;kuchoraC--B;kuchoraC--Bp;kuchoraC--D;kuchoraB--P;choraA--B;kuchoraP--Q;kuchoraB--Q;lebox, 1.2,0,0, SW;leboy, 0,1.2,0, E;leboz, 0,0,1.2, N;nukta A, A, E;nuktaB, B, NW;nuktaB, Bp, NW;nukta C, C, NE;nukta D, D, W;nukta P, P, NE;nuktaQ, Q, S;nukta 1,0,0;asyChukulia kuwa radius ya Dunia ni 1. Kwa kuwa angle BCP 45circ, CP frac1sqrt2.Kwa kuwa angle ACB 135circ, angle PCQ 45circ, hivyoCQ fracCPsqrt2 frac12.Kwa kuwa ndege BPQ ni sawa na overlineAD, angle BQC 90 circ. Na kwa kuwa CB 2 cdot CQ,pembetatu BCQ ni 30circ-60circ-90circ pembetatu. Hasa, angle BCQ 60circ, hivyo angle ACB 120circ. 