Solve each oblique triangle having sides a b c and angles al

Solve each oblique triangle having sides a, b, c and angles alpha, beta, gamma (side a is opposite angle alpha, side b is opposite angle beta, and side c is opposite angle gamma). a = 12 cm, b = 15 cm, c = 20 cm a = 105 degree, a = 8 in, c = 10 In a = 18 ft, b = 22 ft, y = 35 degree

Solution

1)

i)cos=[a²+b²-c²]_/2ab

cos=[12²+15²-20²]_/2*12*15

=94.94^o

cos=[c²+b²-a²]_/2cb

cos=[20²+15²-12²]_/2*20*15

=36.71^o

+ + =180^o

36.71^o+ +94.94^o =180^o

=48.35^o

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ii)

by law of sines a_/sin=b_/sin=c_/sin

8_/sin105^o=b_/sin=10_/sin

8_/sin105^o=10_/sin

sin=(10_/8)sin105^o

=does not exist

no triangle possible

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iii)c²=a²+b²-2abcos

c²=18²+22²-2*18*22cos35^o

c=12.62 ft

by law of sines a_/sin=b_/sin=c_/sin

by law of sines 18_/sin=22_/sin=12.62_/sin35^o

18_/sin=12.62_/sin35^o , 22_/sin=12.62_/sin35^o

sin=(18_/12.62)sin35^o,sin=(22_/12.62)sin35^o

=55^o,=90^o