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Special Right Triangles definitions

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  • 45-45-90 Triangle
    A right triangle with two equal legs and a hypotenuse equal to the leg length times the square root of 2.
  • 30-60-90 Triangle
    A right triangle with side lengths in the ratio: short leg, short leg times square root of 3, and short leg times 2.
  • Hypotenuse
    The longest side in a right triangle, directly opposite the right angle and determined by triangle-specific shortcuts.
  • Leg
    One of the two sides forming the right angle in a triangle; in special cases, its length defines all other sides.
  • Short Leg
    The smallest side in a 30-60-90 triangle, used as the basis for calculating the other two sides.
  • Long Leg
    The side in a 30-60-90 triangle opposite the 60-degree angle, equal to the short leg times the square root of 3.
  • Square Root of 2
    A constant used to relate the legs and hypotenuse in a 45-45-90 triangle, simplifying calculations.
  • Square Root of 3
    A constant used to relate the short leg and long leg in a 30-60-90 triangle, essential for side calculations.
  • Sine
    A trigonometric function representing the ratio of the side opposite an angle to the hypotenuse.
  • Cosine
    A trigonometric function representing the ratio of the side adjacent to an angle to the hypotenuse.
  • Tangent
    A trigonometric function representing the ratio of the side opposite an angle to the side adjacent to it.
  • Cosecant
    A reciprocal trigonometric function, equal to one divided by sine, often simplified in special triangles.
  • Secant
    A reciprocal trigonometric function, equal to one divided by cosine, with predictable values in special triangles.
  • Cotangent
    A reciprocal trigonometric function, equal to one divided by tangent, showing symmetry in special triangles.
  • Reciprocal Identity
    A relationship where a trigonometric function is inverted, leading to simplified values in special right triangles.