Special Right Triangle Theorem

• Right triangle


  Has a right angle<|>Sides of the right angle are the legs<|>Side opposite the right angle is the hypotenuse
• 45-45-90 triangle


  • Two sides are congruent
  • Angles are 45, 45, 90 degrees
• 30-60-90 triangle


  • Angles are 30, 60, 90 degrees
  • Shorter leg is opposite 30 degree angle
  • Longer leg is opposite 60 degree angle
  • Hypotenuse is twice the shorter leg
  • Longer leg is square root of 3 times the shorter leg
• Finding hypotenuse of 45-45-90 triangle

  1. Leg x

  2. Hypotenuse = leg x * square root of 2
• Finding leg of 45-45-90 triangle

  1. Hypotenuse h

  2. Leg = h / square root of 2
• Finding hypotenuse of 30-60-90 triangle

  1. Shorter leg x

  2. Hypotenuse = 2x
• Finding longer leg of 30-60-90 triangle

  1. Shorter leg x

  2. Longer leg = x * square root of 3
• Finding shorter leg of 30-60-90 triangle

  1. Hypotenuse h

  2. Shorter leg = h / 2
• 45-45-90 triangle


  • Leg = 4
  • Hypotenuse = 4 * square root of 2 = 4 * 1.414 = 5.656
• 45-45-90 triangle


  • Hypotenuse = 10
  • Leg = 10 / square root of 2 = 10 / 1.414 = 7.071
• 30-60-90 triangle


  • Shorter leg = 4
  • Hypotenuse = 2 * 4 = 8
  • Longer leg = 4 * square root of 3 = 6.928
• 30-60-90 triangle


  • Hypotenuse = 14
  • Shorter leg = 14 / 2 = 7
  • Longer leg = 7 * square root of 3 = 12.124
• 30-60-90 triangle


  • Longer leg = 24
  • Shorter leg = 24 / square root of 3 = 13.856
  • Hypotenuse = 2 * 13.856 = 27.712
• 45-45-90 triangle


  • Side = 26
  • Hypotenuse = 26 * square root of 2 = 36.768
• Perimeter of 45-45-90 triangle with side 26 is 4 * 26 = 104 units