Answer:
x = 26.244
Step-by-step explanation:
Let the angle opposite the side of length 15 be A and the angle opposite the side with length 18 be B
if a is the side with length 18 and b is the side with length 15
then the relationship between the two know sides a and b and the included angle C is given by the law of cosines
[tex]x^2 = a^2 + b^2 - 2ab \cos(C)[/tex]
[tex]x^2 = 18^2 + 15^ 2 - 2\cdot18\cdot15\cdot\cos(105)[/tex]
[tex]x^2 = 324 + 225 - 540cos(105)[/tex]
cos(105) = -0.2588
[tex]x^2 = 324 + 225 -540(-0.2588)\\[/tex]
[tex]324 + 225 = 549[/tex]
[tex](-540)(-0.2588) = - 139.75[/tex]
[tex]x^2 = 549 - (- 139.75) = 688.75[/tex]
[tex]x^2 = 549 + 139.75 = 688.75[/tex]
[tex]x = \pm\sqrt{688.75} = \pm26.244[/tex]
Since x cannot be negative,
x = 26.244 Answer
