In triangulation, the relation that the sine of an angle is proportional to the opposite side is referred to as which condition?

• A. Law of Sines
• B. Side Condition
• C. Law of Cosines
• D. Ceva's Theorem

Answer: (B)

In triangulation, the key relationship is that the length of a side is proportional to the sine of its opposite angle. This is known as the Law of Sines: a/sin A = b/sin B = c/sin C = 2R, where R is the triangle’s circumradius. Because the ratios to the sines are equal, you can determine unknown distances from measured angles by scaling with the sine values. This law is what lets you connect angles to opposite sides when solving triangles, which is essential in surveying tasks.

The other named ideas don’t describe this particular proportionality. A “Side Condition” isn’t a standard geometric term, the Law of Cosines uses cosines of included angles rather than sines of opposite angles, and Ceva’s Theorem concerns concurrency of cevians, not the proportionality of sides to opposite angles.