DEUXIÈME SOLUTION
Calcul de G.
Calcul de c.
a sin C c = — : — rsin A
log c=Ioja -h log sin G— log sin A log a = 4,8181771
log sin G = 7,4693598 — log sin A = o,3i63oo6
logc = 4,oo38375 c = 4oi64»,o4
Calcul de S.
g 6c sin A
log S=log 6-hlogc-hlogsin A— loga log 6 = 4,9914281 log c = 4,6o38375 .
log sin A = 7, 6836994 ^
— log 2 =7,6989700
log S = 8,9779350 S = 95o4626oo"'«.
TRIANGLES OBLIQUANGLES. Sy
151. Troisième cas. — Résoudre un triangle et trouver sa surface contMissant b = 98"* ,34 ; c = 85" , 78 ; A = 4i'55'i4^7a.
Calcul des angles B et G.
B -h G = iSo* — A. ?^ = 90» — - = 69*^2 aa',64
tg ( -II-) = --^ X cotg -
\ 2 / 0-hC 2
(B — C\ A ) = log (* — c) — log (6 -f- c) -h log cotg-
log (6 — c) = 1,0989896 — log (6 -f- c) =^,7348990 (log (6 -h c) = 2,265ioio) log cotg — = 0,4167309
log tg 1-^ J =7,2606095
Calcul de a.
b sîn A , ..,..,.
TTTIft" *^^ a = log 6 -h log sin A — log sm B
log 6= 1,9927302 log sin A = 7,8248428 -* log sin B = 0,0078531 (log sin B = 7,9921^69)
log a = 1,8254261 a = 66™, 90.
Calcul de la surface.
S—, log S = log 6 + loge -t- log sin A ~ log 3
log 6 = 1,9927302 loge = 1,9333860
log sin A = 7,8248428
— log 2 = 7,6989700
log S = 3,4499290 S = 28i7™«,92ao.
152. Quatriôme cas. — Résoudre un triangle et calculer sa surface connaissant a= ioo",55 ; b = i47'">5i ; c = i28»,67.
S = V^p(p-a) (p-6) ip-c).
p=ri88,265 log p =2,2747696 — log|3 =5,725a3o4
p— a= 87>9*5 log(p— a) = i,944o63o — log (p— a) = 5", 0559370 p— 6= 40,755 log (p— 6) = 1,6101809 — log (p— 6) = 2,3898191 p— c= 59,595 log {p—c) = 1,7752098 — log (p—c) =2,2247902 log S = i[logp -H log(p — a) -f. log (p — 6) -h log ip-^c)]
log p = 2,2747696 ïogfp — a) = i,944o63o log (p — 6) = 1,6101809 log (p — c) = 1,7752098
log S = - (7,6042233) = 3,8021116.
Calcul de A.
Log tg i A = log S — log p — log ip-^a)
log S = 3,8021 116
— Iogp = 3,72523o4
— log (p^a) = 2,0559370
log tg- A =7,5832790 i A = 2o"57'37'',35
Calcul de B.
logtg lB=log S— logp-log (p— 6)
log S = 3,8021116
— lagp = 3,72523o4
—log (p— 6) = 2,3898191
log tg-B =7,9171611
iB = 39*34' 6", 37
Calcul de C.
log tg^C=IogS— logp— log(p— c)
log S = 3,8021116
— Iogp = 3,72523o4
—log (p—c) = 2,2247902
log tg^C= 7,7521322
ic = 29'28'i6'',25
