If Solution 6 given a 33 b 7 c 37 a2 b2 c2 2 b c co

( 6 )

given a = 33 , b = 7 , c = 37

a^2 = b^2 + c^2 - 2 b c cos( A )

cos( A ) = ( b^2 + c^2 - a^2 ) / 2bc

b^2 = a^2 + c^2 - 2 a c cos( B )

cos( B ) = ( a^2 + c^2 - b^2 ) / 2 a c

b^2 = a^2 + c^2 - 2 a c cos( B )

cos( C ) = ( a^2 + b^2 - c^2 ) / 2 a b

Cos( A ) = ( 7^2 + 37^2 - 33^2 ) / ( 2*7*37)

Cos( A ) = 0.63514

A = 50.5696

cos( B ) = ( 33^2 + 37^2 - 7^2 ) / (2*33*37)

Cos(B) = 0.98649

B = 9.42877915274

cos( C ) = ( 33^2 + 7^2 - 37^2 ) / ( 2*33*7)

Cos(C) = -0.5

C = 120

( 4 )

given A = B = 35 , a = ?

A + B + C = 180

C = 180 - ( A + B)

C = 180 - 70

C = 110

a/sin(A) = c/sin(C)

a = c sin(A) / sin(C)

a =13 ( sin(35) / sin(110) )

a = 7.9350348269

( 5 )

cos (30 ) = 10 / x

x = 10 / cos(30)

x = 10 / ( sqrt(3) / 2)

x = 20 / sqrt(3)

cos( 150 ) =10 / x ===> adjacent side / hypotnuese

- sqrt(3) / 2 = 10 / x

x ==> 10 /( - sqrt(3) / 2 ) ==> 20 / - sqrt(3)