The 3 little division "sums" that are the Sine and its brother ratios, Cosine and Tangent, given in any basic right-angled triangle, form the basis for the entire, vast field of Trigonometry and its uses, going far beyond simple Plane Geometry into such things as Harmonic Analysis (Sine functions of amplitude with respect to time), the Laws of Electricity (starting with the phase angle between Volts and Current in a.c. circuits, etc.), and so on.
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The law of sines refers to a relationship between the sides and the angles of a triangle. Consequently, it is used in trigonometry and, to a lesser extent, in geometry. It is not really relevant in calculus or statistics.
Trigonometry mainly but also geometry, algebra.
Yes, the law of sines can be used in a right triangle. The law applies to any arbitrary triangle.
Yesterday's date cannot be used.
No, it does not.