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.
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,
![c=\sqrt{a^{2}+ b^{2}-2ab.cos \theta }](https://tex.z-dn.net/?f=c%3D%5Csqrt%7Ba%5E%7B2%7D%2B%20b%5E%7B2%7D-2ab.cos%20%5Ctheta%20%7D)
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,
![AB=\sqrt{(AC)^{2}+(B C)^{2} -2(AC)(BC).Cos(51.2)^{o} }](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28AC%29%5E%7B2%7D%2B%28B%20C%29%5E%7B2%7D%20-2%28AC%29%28BC%29.Cos%2851.2%29%5E%7Bo%7D%20%20%7D)
![AB=\sqrt{(80)^{2}+(104)^{2} -2(80)(104).Cos(51.2)^{o} }](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%2880%29%5E%7B2%7D%2B%28104%29%5E%7B2%7D%20-2%2880%29%28104%29.Cos%2851.2%29%5E%7Bo%7D%20%20%7D)
![AB=\sqrt{6400+10816 -16640.Cos(51.2)^{o} }](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B6400%2B10816%20-16640.Cos%2851.2%29%5E%7Bo%7D%20%20%7D)
![AB=\sqrt{7328.4}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B7328.4%7D)
AB = 25.6 yd
Hence, the distance between A and B is 85.6 yds.
Learn more about the Law of Cosine:
brainly.com/question/17289163
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Answer:
No
Explanation:
An example of an amphibian would be frogs. Also, chickens are birds. ;)
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