Lesson: Geometry - 21

30°/60°/90° Triangles

[Page 21 of 30]

A triangle where the angles are 30°, 60°, and 90°. If you draw an altitude in an equilateral triangle, you will form two congruent 30º- 60º- 90º triangles. Starting with the sides of the equilateral triangle to be 2, the Pythagorean Theorem will allow us to establish pattern relationships between the sides of a 30º- 60º- 90º triangle. These relationships will be stated here as "short cut formulas" that will allow us to quickly arrive at answers regarding side lengths without applying trigonometric functions, or other means.

Another triangle that you're almost sure to see on your standardized test is the 30°/60°/90° triangle. Often, you'll see it when an equilateral triangle is divided into two triangles of equal size. Learn the side-length ratio for the 30°/60°/90° triangle and you'll save yourself many calculations on test day.

If we set x as the length of the shortest side (the side opposite the 30° angle), then the side opposite the 60° angle has length x √3, and the hypotenuse has length 2x.

Hint

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