legs

(noun)

The sides adjacent to the right angle in a right triangle.

Related Terms

  • hypotenuse
  • right triangle
  • Pythagorean theorem

Examples of legs in the following topics:

  • The Distance Formula and Midpoints of Segments

    • This formula is easily derived by constructing a right triangle with the hypotenuse connecting the two points ($c$) and two legs drawn from the each of the two points to intersect each other ($a$ and $b$), (see image below) and applying the Pythagorean theorem.
    • The distance formula includes the lengths of the legs of the triangle (normally labeled $a$ and $b$), with the expressions $(y_{2}-y_{1})$ and $(x_{2}-x_{1})$.
  • Right Triangles and the Pythagorean Theorem

    • The sides adjacent to the right angle are called legs (sides $a$ and $b$).
    • The sum of the areas of the two squares on the legs ($a$ and $b$) is equal to the area of the square on the hypotenuse ($c$).  
  • Slope

    • Count the rise on the vertical leg of the triangle: 4 units.
    • Count the run on the horizontal leg of the triangle: 5 units.
  • Pythagorean Identities

    • The legs are $x$ and $y$.
  • Scientific Applications of Quadratic Functions

    • This says that the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the two legs ($a$ and $b$) of the triangle.
  • Parabolas As Conic Sections

    • The focal length is the leg of the right triangle that exists along the axis of symmetry, and the focal point is the vertex of the right triangle.
  • Defining Trigonometric Functions on the Unit Circle

    • Note that the values of $x$ and $y$ are given by the lengths of the two triangle legs that are colored red.
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