What is 90 60 30 triangle?

A 30-60-90 triangle is a special right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees. It has several distinctive properties:

• Angle Measures: By definition, the angles are 30°, 60°, and 90°.

• Side Ratios: The sides are in a specific ratio of 1 : √3 : 2. If the side opposite the 30° angle (the shorter leg) has length x, then:

  • The side opposite the 60° angle (the longer leg) has length x√3.
  • The hypotenuse (the side opposite the 90° angle) has length 2x.

• Relationship to Equilateral Triangles: A 30-60-90 triangle is exactly half of an equilateral%20triangle, cut along its altitude.

• Applications: 30-60-90 triangles frequently appear in trigonometry and geometry problems. Their predictable side ratios make them useful for calculations and proofs. You can easily find the length of any side if you know at least one side length.