CST Level 1 Land Surveyor Certification Practice

Which term describes a method of determining unknown distances in the Missing Line Method?

1. Law of sines

2. Law of cosines

3. Law of averages

4. Law of tangents

The correct answer is: Law of cosines

In the context of the Missing Line Method, the Law of Cosines is particularly relevant and effective for determining unknown distances in a triangle when two sides and the included angle, or all three sides, are known. This law states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. This relationship is crucial in surveying and triangulation, especially when precise calculations are needed for unknown distances. As surveyors often work on triangular setups, the Law of Cosines allows for accurate computation that accounts for the geometry involved, making it the correct choice for this method of determining distances. The Law of Sines is also a method used in triangles but applies under different circumstances and is typically utilized when two angles and one side are known, rather than when the relationship between three sides and the angles is crucial. The Law of Averages pertains more to statistical calculations and is not relevant to geometric measurements, while the Law of Tangents deals with angles in triangulation as well but is not the principal method for determining unknown distances in the context of this particular question.