The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The distance between A and B is 85.6 yds.
What is the Law of Cosine?
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
The three points A, B, and C will form a triangle. Therefore, using the law of cosine the measure of the third side AB can be written as,
[tex]AB =\sqrt{(AC)^2 + (BC)^2 -2(AC)(BC)\cdot \cos(51.2^o)}\\\\AB =\sqrt{(80)^2 + (104)^2 -2(80)(104)\cdot \cos(51.2^o)}\\\\AB = \sqrt{6400+10816-16640\cos51.2^o}\\\\AB = \sqrt{7328.4}\\\\AB=85.6\rm\ yd[/tex]
Hence, the distance between A and B is 85.6 yds.
Learn more about the Law of Cosine:
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