Identify a 30-60-90 Right Triangle: Key Properties Explained

Learn how to identify a 30-60-90 right triangle by its unique angles and side ratios.

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A right triangle is identified as a 30-60-90 triangle by its unique angle and side ratio properties. In this triangle, the angles are indeed 30, 60, and 90 degrees. The side lengths follow a specific ratio: the shortest side (opposite the 30° angle) is half the hypotenuse, and the longer leg (opposite the 60° angle) is the short side times √3. For example, if the short side is 1, the hypotenuse is 2, and the longer side is √3.

FAQs & Answers

  1. What are the characteristics of a 30-60-90 triangle? A 30-60-90 triangle has angles of 30°, 60°, and 90°, with side lengths in a specific ratio: 1 : √3 : 2.
  2. How do you find the sides of a 30-60-90 triangle? To find the sides, take the shortest side as 1, then the hypotenuse is 2, and the longer leg is √3 times the shortest side.
  3. What is the formula for 30-60-90 triangles? In a 30-60-90 triangle, the relationships are: shortest side = x, longer leg = x√3, hypotenuse = 2x.
  4. Can you give an example of a 30-60-90 triangle? If the shortest side (opposite 30°) is 1, then the hypotenuse is 2, and the longer leg (opposite 60°) is √3.

Watch More

For a deeper understanding of triangle properties, check out our videos on equilateral triangles and isosceles triangles.

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  3. Is a 30-60-90 Triangle Isosceles? Discover why a 30-60-90 triangle cannot be isosceles, including definitions and side ratios.
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