30-60-90 Triangles                    Page 2 of 5

​Relationship Between the
​Short Leg and Hypotenuse

The short leg of a 30-60-90 triangle is always 1/2 the length of the hypotenuse.  You could also switch it around and say that the hypotenuse is always twice the length of the short leg.

Remember, a 30-60-90 triangle is half of an equilateral triangle.  It can help to sketch in where the rest of the equilateral triangle would be to help you figure out the missing side length.

Example 1
Find a.

Answer:
It can be helpful to sketch in the rest of the equilateral triangle to make it easier to see the relationship between the short leg and the hypotenuse. The side across from the right angle is the hypotenuse (the 14) and we need to find the short leg (remember, the legs form the L to make the 90 degree angle).  We know that the hypotenuse is 14.  This means the the short leg (the a) is half of 14.   a = 7

Example 2
Find b.

Answer:
It might help to sketch in the rest of the equilateral triangle to help you see the relationship between the two sides.  The legs always form the 90 degree corner and the hypotenuse is always across from the right angle.  This means we know the short leg is 4 and we need to find the hypotenuse.  The hypotenuse is always twice as long as the short leg so we can just multiply 4 by 2 to get b.  b = 8

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