Verified answer

Law of Cosines

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

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

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

The method is called the law of cosines:

C^2 = A^2 + B^2 - 2AB cosine of the angle between A and B

the pythagrian theorum is a special case where the angle is 90 degrees so the cosine is 0.

for the purpose of this C is the unknown side.

C^2 = (15^2) + (9^2) - 2(15)(9) cosine 120 degrees.

C^2 = 225 + 81 - 270( -.5)

( angle greater than 90 degees has a - cosine)

C^2 = 225 +81 + 135 = 441

C= 21Cm

Law of Cosines

AC=b

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

b^2=15^2+9^2-2(15)(9) cos(120)

b^2=225+81-270cos(120)

b^2=306-27(-0.5)

=306+13.5

=219.5

AC=b=sqrt(319.5)=17.8745 cm

You may round it to the desired number of decimals.

use cosine laws

here...

b^2 = a^2 + c^2 - 2.a.c.cos B

just subst the given value.

thx