Answer:
[tex]c=11.49[/tex]
Step-by-step explanation:
It is given that a = 5, b = 12, and c = 72°, then using the cosine formula, we get
[tex]c^2=a^2+b^2-2abcosC[/tex]
[tex]c^2=(5)^2+(12)^2-2(5)(12)Cos72^{\circ}[/tex]
[tex]c^2=25+144-2(60)(0.309)[/tex]
[tex]c^2=169-37.08[/tex]
[tex]c^2=131.92[/tex]
[tex]c=\sqrt{131.92}[/tex]
[tex]c=11.49[/tex]
Therefore, the value of the length of the side c is 11.49.