30-60-90/45-45-90 Triangle Relationships

30-60-90 Triangles

The side opposite the 30 degree angle is the short side. Let’s start there. This side is half of the hypotenuse…or you could say the hypotenuse is two times the short side. The hypotenuse is the longest side. That leaves the side opposite the 60 degree angle….the middle side. It is always √3 times the short side. In other words:

Short Side = x
Medium Side = √3 x
Long Side = 2x
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45-45-90 Triangles

The two sides opposite the 45 degree angles are congruent. The third side is √2 times the shorter sides.

Both Congruent Sides = x
Hypotenuse = x √2

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