B 63 degree 30 a 122 ft c 78 ft A b 132 ft A 73 degree

B = 63 degree 30\' a = 12.2 ft c = 78 ft A) b = 13.2 ft, A = 73 degree 07\', C = 37 degree 23\' B)b = 11.2 ft, A = 77 degree 49\', C = 38 degree 41\' C)b = 12.2 ft, A = 75 degree 07\', C = 41 degree 23\' D) No triangle satisfies the given conditions a = 20 ft b = 38 ft C = 42 ft Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. a = 47 ft b = 59 ft c = 65 ft

Solution

19)

by law of cosines

b²=a²+c²-2accosB

b²=12.2²+7.8²-2*12.2*7.8cos63.5^o

b²=124.7596322

b=11.17

b=11.2ft

by law of sines a_/sinA=b_/sinB=c_/sinC

12.2_/sinA=11.2_/sin63.5=7.8_/sinC

A=77.82^o=77^o49\',C=38.67^o=38^o41\'

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20)

a=20ft , b=38ft ,c=42ft

by law of cosines

cosA=(b²+c²-a²)_/2bc

cosA=0.8797

A=28.39^o

cosB=(a²+c²-b²)_/2ac

B=64.62^o

cosC=(a²+b²-c²)_/2ab

C=86.98^o

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21)

a=47, b=59, c=65

s=(a+b+c)_/2

s=85.5

area of triangle=[s(s-a)(s-b)(s-c)]

area of triangle=[85.5*(85.5-47)*(85.5-59)*(85.5-65)]

area of triangle= 1337.3 square ft