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 measure of side DE is 12.3.
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.
In the given triangle the length of the side DE can be found using the law of cosine. Therefore, the length of the side DE can be written as,
DE² = DF² + EF² - 2(EF)(DF)(Cos 59°)
DE² = 144 + 169 - 2(12 × 13 × Cos 59°)
DE² = 144 + 169 - 160.6918
DE² = 152.30812
DE = 12.3413 ≈ 12.3
Hence, the measure of side DE is 12.3.
Learn more about the Law of Cosine:
https://brainly.com/question/17289163
#SPJ5
