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  2. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...

  3. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    Heron's formula. A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths ⁠ ⁠ ⁠ ⁠ ⁠ ⁠ Letting ⁠ ⁠ be the semiperimeter of the triangle, the area ⁠ ⁠ is [1] It is named after first-century engineer Heron of Alexandria (or Hero) who ...

  4. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of ...

  5. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

  6. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Law of cosines. Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite ...

  7. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    Trigonometry. 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 ...

  8. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    v. t. e. 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.

  9. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    Euler's theorem: In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1][2] or equivalently where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who ...

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