Law of sines

Laser triangulation method is a technique which uses the law of sine to find the coordinates and distance of an unknown point by forming a triangle with it and two known reference points [2]. In Fig. 12.8, A and B are the two reference locations given by the camera and the sensor locations, and C is the location of the object point of interest. The distance from A to B can be measured as c, and the angles a and P can also be measured. Following the law of sine the distances a and b can be calculated. The coordinates of A and B are known, then the coordinate of C can also be calculated. The same principle is employed in various other scaiming methods. 

For regular SW refraction on a planar CS, the following relationships ("the law of sines") hold true for the projections of velocities onto a CS plane (Fig. lb). 

From (8.4) and the IBrst form of (8.S), the interfadal tensions and the supplements of the contact angles are related to eadi other as the sides and angles of the triangle in Fig. 8.2. This is Neumaim s triang e. The first equality in (8.5) and the two others obtained from it by permutation aSet, P, and y, are the law of cosines applied to this triangle (8.4) and its permutations are the law of sines. 

The fundamental theorems and laws of trigonometry are frequently used by engineers. Three of the most frequently used relationships are the Pythagorean theorem, the Law of Sines, and the Law of Cosines. 

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