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  2. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    Construct a second triangle with sides of length a and b containing a right angle. By the Pythagorean theorem, it follows that the hypotenuse of this triangle has length c = √ a 2 + b 2, the same as the hypotenuse of the first triangle. Since both triangles' sides are the same lengths a, b and c, the triangles are congruent and

  3. Hypotenuse - Wikipedia

    en.wikipedia.org/wiki/Hypotenuse

    In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. [7] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem. It states that the sum of the two legs squared equals the hypotenuse

  4. Pythagorean addition - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_addition

    In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides.According to the Pythagorean theorem, for a triangle with sides and , this length can be calculated as = +, where denotes the Pythagorean addition operation.

  5. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    the third side of a triangle if two sides and an angle opposite to one of them is known (this side can also be found by two applications of the law of sines): [a] = ⁡ ⁡. These formulas produce high round-off errors in floating point calculations if the triangle is very acute, i.e., if c is small relative to a and b or γ is small compared to 1.

  6. Right triangle - Wikipedia

    en.wikipedia.org/wiki/Right_triangle

    A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).

  7. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]

  8. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    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 from the vertex opposite the base onto the line containing the base.

  9. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS). For all cases in the plane, at least one of the side lengths must be specified.