TYPES DE CALCUL POUR LA RÉSOLUTION DES TRIANGLES
TRUNQLES RECTANGLES.
145. Premier cas. — Résoudre un triangle rectangle connaissant a= 55-, B = 53* 7' 48'',4.
Calcul derC.
Caleul de b.
6 = a sin B
\og 6 == log a + log 8În B
loga= i,74o36a7
log sin B = 7, 9030901
log b = 1,6434528 6 = 44».
Calcul de e.
c = a cos B
log c = log a + log cos B
loga:= 1,7403637
log cos B =T,778i5i2
loge = i,5i85i39 c = 33».
146. Deuxième cas. — Résoudre un triangle reotangh connaissant b = 7",52 etB=z 25*i7'i4^
• Calcul de C.
Calcul de a.
sinB log a = log 6 — logsÎQ B
log 6 = 0,8762178
— . log sin B = 0,3694135 (log sin B =*î,63o5867^
log a =1,24563x1 a = i7",6o.
Calcul de c. .
c = 6 cotg B log c = log 6 + log cotg B
log 6 = 0,8762178 log cotg B = 0, 5256671
log c = 1,2018849 e = i5"^,92 (par excès).
147. Troisième cas. — Résoudre un triangle rectangle eonnmtvant a= o" 64, b = o»,3i.
Calcul de B etc.
sin B = cos C = -
log sin B = lôg C8B C = lûg &»log a
log6 = T,49i36i7
log sin B=T,685i8i7 B = 28''58'l7^5 C = 6i* i'4a',5.
Cakul de e.
Ijg c = - [log (a -f- 6) -*- log (a — -ft^
log (a -f- 6) =7,977723^ Log (a — 6) =T,5i85i59,
2 log c= 1,4962375
lO^r 0 = 7,7481187
C = o™,56 (par excès).
148. Quatrième cas. — Résoudre un trimiglff ret^ngiBi connaissant b = gS'*, c = 124°^.. ^
Calcul de B et de C.
tgB=.cotgC^-
log tg B = log cotg G = loj^: 6 — log c
log 6=2,9^^829
— kàg c = 5^9^65783 (log c = 3,0954317)
log Vx B = T, S75061 3 JB = 3«"52'ii\6.
Calcul d^ a.
sin B
log a = I©g 5 — leg siû B Wg 6 =1^9684849
— log sin B = 0^25118488^ ^og sin B =7,7781512)
k^ a = &, i>9o33i7 0,= lâô™.
TRIANGLES OBLIQUÂNGLES. 55
TRIANGLES OBLIQUANGLES.
149. Premi::,r cas. — Résoudre un triangle et calculer sa surface connaissant B = 68''26'i7''; G = 75*8'a3''j
Calcul de À.
Ajr= i8o* — (B H- C) = 56«25'2o'.
^ Calcul de b.
, a sin B
siû A
log ô = log a -h log sin B — log sin A
log a= 1,9907385 log sin B = T, 9684927 __
— log sin A = 0, 2264103 (log sin A = 1,7735897)
log b = 2,i8564i3 6 = i53°^,33.
Calcul de c.
a sîn G
c = — : — r~ sin A
log c = log a -h log sin C — log sin A
logo= 1,9907383
log sin C =7,9862262
— log sin A = G, 2264 1 o3
log c = 2,2023748 c = i59%36.
Calcul de la sur'face,
__ a' sin B sin C
^ 2 sin (B -f- G) log S = 9 log a + log sin B -*- log sin C — log a — log sin (B -h C)
a log 0 = 3,9814766
log sin B = 7,9684927 log sin C =7,9862262
—-log a = 7,6989700 — log sin (B -h G) =o,2864io5
log S = 3,8605768 S = 7253«»,97.
160. Deuxième cas. — Résoudre un triangle et calculer sa surface connaissant a = 65792" ,60 ; b = o8o45'",6o • ' A = 28'5i'48^6.
Calcul de B.
sin B =
ôsinA
log sin B = log 6 -t- log sin A — log a log 6 = 4,9914281
log sin A =7,6836994
— log 0 = 5, 1818329 (log a = 4,8181771)
log sin B =7,8569604
Il 7 a deux solutions :
