4. Find the greatest angle of the triangle in which the sides are 5, 6, 7; given log 6=7781513, L cos 39° 14' 9.8890644, diff. for 1'=1032. 5. If a=3, b=175, c=2.75, find C; given log 2, 6. If the sides are 24, 22, 14, find the least angle; given 7. Find the greatest angle when the sides are 4, 10, 11; given log 2, log 3, L cos 46° 47'=9-8355378, diff. for 1'=1345. 8. If a b c = : 15 13:14, find the angles; given log 2, log 3, log 7, I tan 26° 33' 9'6986847, diff. for 1'=3159, Z tan 29° 44′=9.7567587, diff. for 1'=2933. 9. If a b c 3 : 4:2, find the : L tan 14° 28′ = 9.4116146, angles; given log 2, log 3, diff. for 10′′=870, L tan 52° 14'10.1108395, diff. for 10"-435. 189. To solve a triangle having given two sides and the included angle. Let the given parts be b, c, A, and let tan Example 1. If the sides a and b are in the ratio of 7 to 3, and the included angle C is 60°, find A and B; given Example 2. If a=681, c=243, B=50° 42', solve the triangle, by the use of Tables. Thus A=109° 39′ 57′′, C=19° 38′ 3′′, b=559'63. 190. From the formula tan B-C b-c A cot 2.7479012 it will be seen that if b, c, and B-C are known A can be found; that is, the triangle can be solved when the given parts are two sides and the difference of the angles opposite to them. EXAMPLES. XVI. c. 1. If a=9, b=6, C=60°, find A and B; given log 2, log 3, I tan 19° 6' 9.5394287, Ltan 19° 7′ = 9.5398371. 2. If a=1, c=9, B=65°, find A and C'; given log 2, L cot 32° 30'=10.1958127, L tan 51° 28′ =100988763, diff. for 1'=2592. 3. If 17a-7b, C=60°, find A and B; given log 2, log 3, L tan 35° 49′=9.8583357, diff. for 10"=2662. 4. If b=27, c=23, A=44° 30′, find B and C'; given log 2, L cot 22° 15'=10.3881591, I tan 11° 3' 9.2906713, diff. for 1'=6711. 5. If c=210, a= given log 2, = =110, B=34° 42′ 30′′, find C and A; L cot 17° 21′ 15′′-10.5051500. 6. Two sides of a triangle are as 5: 3 and include an angle of 60° 30': find the other angles; given log 2, L cot 30° 15'10.23420, L tan 23° 13′ = 9.63240, diff. for l'=35. 7. If a=327, c=256, B=56° 28′, find A and C; given L tan 61° 46'-10-2700705, L tan 12° 46′ = 9.3552267, diff. for 1'=5859. 8. If b=4c, A=65°, find B and C; given log 2, log 3, I tan 43° 18′ 9.9742133, = diff. for 1'=2531. 9. If a=23031, b=7677, C=30° 10′ 5′′, find A and B ; given log 2, L tan 15° 5' 9'4305727, diff. for 10"=838, 191. To solve a triangle having given two angles and a side. Let the given parts be denoted by B, C, a; then the third angle A is found from the equation A=180° – B – C, and b= a sin B .. log b=loga + log sin B-log sin A; whence b may be found. Similarly, c may be obtained from the equation log c=log a+log sin C-log sin A. Example. If b=1000, A=45°, C=68° 17′ 40′′, find the least side, having given 1 log 2=3010300, log 7·69868864118, diff. for 1=57, L sin 66° 42'9.9630538, diff. for 1'=544. 1. If B=60° 15′, C=54° 30′, a=100, find c; given I sin 54° 30′ =9.9106860, log 8.9646162=9525317, |