Triangulation can be used to find the distance from the shore to the ship. The observer at α measures the angle between the shore and the ship, and the observer at β does likewise. If the length l is known, then the law of sines can be applied to find the distance d.

In trigonometry and elementary geometry, triangulation is the process of finding a distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other reference points. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane. ... Wikibooks has more about this subject: Trigonometry Table of Trigonometry, 1728 Cyclopaedia Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ... Table of Geometry, from the 1728 Cyclopaedia. ...

Some identities often used (valid only in flat or euclidean geometry): Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...

• The sum of the angles of a triangle is π rad or 180 degrees.
• The law of sines
• The law of cosines
• The Pythagorean theorem

Triangulation is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision and gun direction of weapons. The mathematical constant π ≈ 3. ... The radian (symbol: rad, or a superscript c ( half circle)) is the SI unit of plane angle. ... In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane. ... In trigonometry, the law of cosines (also known as the cosine formula) is a statement about a general triangle which relates the lengths of its sides to the cosine of a known angle. ... The Pythagorean theorem: The sum of the areas of the two squares on the legs (blue and red) equals the area of the square on the hypotenuse (purple). ... Surveyor at work with a leveling instrument. ... There are several traditions of navigation. ... Metrology is variously described as the science of measurement; the science of accuracy and precision; the history of measures; the history of measurement and other definitions. ... This article does not cite its references or sources. ... Binocular vision is vision in which both eyes are used synchronously to produce a single image. ... The bayonet, still used in war as both knife and spearpoint. ...

Many of these surveying problems involve the solution of large meshes of triangles, with hundreds or even thousands of observations. Complex triangulation problems involving real-world observations with errors require the solution of large systems of simultaneous equations to generate solutions. A mesh is similar to fabric or a web in that it has many connected or weaved pieces. ... In mathematics, simultaneous equations are a set of equations where variables are shared. ...

Famous uses of triangulation have included the retriangulation of Great Britain. In 1935, the new Director General of the Ordnance Survey, Major-General Malcolm MacLeod, started the retriangulation of Great Britain, an immense task which involved erecting concrete triangulation pillars (trig points) on prominent hilltops throughout Great Britain. ...

See also

• Multilateration, where a point is calculated using the time-difference-of-arrival between other known points
• Parallax
• Trilateration, where a point is calculated given its distances from other known points
• Trigonometry