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  .
Many engineers and scientists are comfortable with use of the Law of Sines
, which permits calculation of the length of all sides and magnitude of all angles in a triangle if the length of one side and magnitude of two angles are known.
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
. Topics increase in mathematical complexity as the book progresses to encompass dozens of examples including a derivation of the Euler-Lagrange equation, heat flow and analytic functions, and a bicycle wheel and the Gauss-Bonnet theorem.
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.