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.

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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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