Diagram for the derivation of the law of sines
for plane triangles.
Instead of the textbook proof, the authors have worked to start with the dynamic visual proof that is based on the static geometrical proof of the law of sines
published in  .
Per FIGURE 1, if the length of side A and angles b and c are known, the Law of Sines
allows the length of sides B and C to be calculated:
Levi's first case demonstrates how a fish tank with a right-triangular cross-section is a physical system embodying the Pythagorean theorem and also how it implies the law of sines
This is determined by using the law of sines
to determine the sides and angles of the triangle formed by the ground station, the satellite, and the center of the Earth.
Then by the law of sines
, applied to triangle ABC we have
While there are many trigonometric formulas, the three most commonly used in EW applications are the Law of Sines
, the Law of Cosines for Angles, and the Law of Cosines for Sides.