30-60-90 Triangle

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A 30-60-90 triangle is a form of a right triangle (a triangle that has one 90-degree angle) with sides in the ratio 1:√3:2. This suggests that the leg of the triangle that is shorter is half the length of the hypotenuse (the longest leg), and the longer leg is √3 times the length of the leg that is shorter.

The following are the properties of a 30-60-90 triangle:

  • It has a right angle of 90 degrees.
  • The sides of this triangle are in the ratio 1:√3:2.
  • The leg that is shorter is half the length of the hypotenuse.
  • The leg that is longer is √3 times the length of the shorter leg.
  • The hypotenuse of the triangle is two times the length of the shorter leg.

30-60-90 triangles have very special significance in geometry because they have many crucial properties that are useful in problem-solving. As an example, the angles and side ratios of a 30-60-90 triangle are always the same, no matter what ‌the size of the triangle is. This property is very useful in solving problems involving 30-60-90 triangles as you will not have to worry about the exact lengths of the sides.

30-60-90 triangles are also useful in real-world applications, such as in construction and engineering, where they are used to design and build structures that need to be strong and stable.

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