Triangles and transformations
Two sides with the angle between them means cosine law; an angle paired with its opposite side means sine law.
A worked example
Sides 10 m and 7 m with 48° between them give c^2 = 10^2 + 7^2 - 2(10)(7)cos 48° = 55.3, so c = 7.4 m.
The mistake people actually make
Rotations, reflections and translations keep size and shape and change only position or orientation. Only a dilation resizes the figure, multiplying every length by the scale factor.