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 correct option is B.
<h3>What is the Law of Cosine?</h3>
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\cdot Cos\theta}](https://tex.z-dn.net/?f=c%20%3D%5Csqrt%7Ba%5E2%20%2B%20b%5E2%20-2ab%5Ccdot%20Cos%5Ctheta%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 length of the sidelink b using the cosine rule can be written as,
![b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7Ba%5E2%2Bc%5E2-2ac%5Ccos%28%5Cangle%20B%29%7D%5C%5C%5C%5Cb%20%3D%20%5Csqrt%7B4%5E2%2B5%5E2%20-%202%284%29%285%29%28%5Ccos%2060%5Eo%29%7D%5C%5C%5C%5Cb%20%3D%20%5Csqrt%7B16%2B25-20%7D)
Hence, the correct option is B.
The complete question is:
Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?
Options are given in the image below.
Learn more about the Law of Cosine:
brainly.com/question/17289163
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