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Unit 7 · Right Triangles and Trigonometry

7.630-60-90 Triangles

Quick Answer

In a 30-60-90 triangle, the side ratios are 1 : √3 : 2 (short leg : long leg : hypotenuse). Given any one side, the other two can be found using these ratios.

Essential Question

How do the 30-60-90 side ratios follow from an equilateral triangle cut in half, and how do you use them to find missing sides?

Learning Goals

  • 1State the 30-60-90 side ratios.
  • 2Find missing sides given the short leg, long leg, or hypotenuse.
  • 3Recognize 30-60-90 triangles in context.
  • 4Apply 30-60-90 ratios to real-world problems.

Key Vocabulary

30-60-90 triangle

A right triangle with side ratios 1 : √3 : 2 (short leg : long leg : hypotenuse).

Short leg

The side opposite the 30° angle; half the hypotenuse.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.