The law of cosine helps us to know the third side of a triangle. The value of third side c is 20.87.
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.
Given, in ΔABC, a = 32, b = 21 and the angle between a and b is 40°, therefore, the value of ∠C=40°.
Now, the value of the third side of the triangle using the cosine law can be written,
[tex]c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}\\\\c=\sqrt{32^{2}+21^{2}-2(32 \times 21)\cdot \cos 40^o}\\\\c=\sqrt{1,024+441-1,029.5637}\\\\c=20.867 \approx 20.87[/tex]
Hence, the value of third side c is 20.87.
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