The direction of the boat sail to head directly back to the marina which leaves the marina and sails 13 miles northeast, then 12 miles east is 23.45° W of S.
What is the law of cosine?
When the three sides of a triangle is known, then to find any angle, the law of cosine is used.
It can be given as,
[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]
Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.
A boat leaves the marina and sails 13 miles northeast, then 12 miles east. The image of the problem is attached below.
Thus, the value of the third side is,
[tex]c=\sqrt{12^2+13^2-(2\times12\times13\times \cos 135)}\\c=23.01[/tex]
The measure of the angle x is,
[tex]\angle x=\cos^{-1}\dfrac{23.1^2+13^2-12^2}{2\times23.1\times13}\\\angle x=23^o26'57"\\\angle x=23.449^o[/tex]
Thus, the direction of the boat sail to head directly back to the marina which leaves the marina and sails 13 miles northeast, then 12 miles east is 23.45° W of S.
Learn more about the law of cosine here;
https://brainly.com/question/4372174
