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  2. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    To find an unknown angle, the law of cosines is safer than the law of sines. The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the ...

  3. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

  4. Triangulation - Wikipedia

    en.wikipedia.org/wiki/Triangulation

    In China, Pei Xiu (224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances, [5] while Liu Hui (c. 263) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.

  5. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Trigonometry (from Ancient Greek τρίγωνον (trígōnon) ' triangle ' and μέτρον (métron) ' measure ') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.

  6. Mathematical discussion of rangekeeping - Wikipedia

    en.wikipedia.org/wiki/Mathematical_discussion_of...

    The observer would first use this device to measure the angular width of the target. Knowing the angular width of the target, the range to the target, and the known length of that ship class, the angle on the bow of the target can be computed using equations shown in Figure 2. Human observers were required to determine the angle on the bow.

  7. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Angle trisection is the construction, using only a straightedge and a compass, of an angle that is one-third of a given arbitrary angle. This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8]

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