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Side Lengths of the Unit Triangles

Author:Lauren Duncan, Auston B Cron, WheelerELHS

Since the Unit Circle has radius of 1 unit, the special right triangles that exist in the Unit Circle all have a hypotenuse of 1 unit.

We can determine the side lengths of each special right triangle within the Unit Circle. Each square root expression has been converted to decimal form for your reference. Notice the labeled side lengths on each triangle. The applet also shows calculated side length ratios within each triangle. Click "Unitize" to make the hypotenuse equal to 1 (as it would be in the Unit Circle) Unitize each of the triangles to determine the side length values used in the Unit Circle.

Which of the following side lengths exist within the "unitized" version of the 45-45-90 triangle?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Which of the following side lengths exist within the "unitized" version of the 30-60-90 triangle?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

In the 45-45-90 triangle, both LEGS are equal to ________________.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

In the 30-60-90 triangle, the SHORT LEG is equal to ________________.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

In the 30-60-90 triangle, the LONG LEG is equal to ________________.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

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