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Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.

We don't know what type of a triangle we're considering here. Therefore the universal and quickest solution to the first problem is use of the cosine rule, which states that for a triangle with sides a,b and c and the angle θ between sides “a” and “b”:

c2=a2+b2-2*a*b*cos(θ)

To find the area of the triangle we should use the formula:
 
A=1/2*a*b*sin(θ)

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