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  2. Clock angle problem - Wikipedia

    en.wikipedia.org/wiki/Clock_angle_problem

    A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. [1]

  3. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    The problem of calculating angle is a standard application of Hansen's resection. Such calculations can establish that ∠ B E F {\displaystyle \angle {BEF}} is within any desired precision of 30 ∘ {\displaystyle 30^{\circ }} , but being of only finite precision, always leave doubt about the exact value.

  4. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal.

  5. Angle trisection - Wikipedia

    en.wikipedia.org/wiki/Angle_trisection

    For example, ⁠ 3 π / 7 ⁠ is such an angle: five angles of measure ⁠ 3 π / 7 ⁠ combine to make an angle of measure ⁠ 15 π / 7 ⁠, which is a full circle plus the desired ⁠ π / 7 ⁠. For a positive integer N , an angle of measure ⁠ 2 π / N ⁠ is trisectible if and only if 3 does not divide N .

  6. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  7. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ⁡ ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...