Special Right Triangles 30º-60º-90º

 

Certain triangles possess "special" properties that allow us to use "short cut formulas" in arriving at information about their measures.  These formulas let us arrive at the answer very quickly. One such triangle is the 30º-60º-90º triangle. There are two "special" formulas that apply ONLY to the 30º-60º-90º triangle.

 

30º-60º-90º "Special" Formulas
H = hypotenuse
LL = long leg (across from 60º)
SL = short leg (across from 30º)

You must remember that these formulas can be used ONLY in a 30º-60º-90º triangle.

 

Using the formulas:

EASY: Find x and y. x is the short leg Answer y is the long leg Answer

 

 

HARDER: Find x and y. 6 is the short leg and x is the hypotenuse (start with what you have given) Answer y is the long leg Answer

 

 

HARDEST: (requires more algebraic manipulation) Find x and y. 8 is the long leg and  x is the hypotenuse (start with what you have given) Answer y is the short leg Answer

 

What if I forget the formulas? What should I do?

There is always more than one way to tackle a problem.  If you forget these formulas, you could always use the Trigonometry formulas to find one of the missing sides and then use the Pythagorean Theorem to find the last side OR you could use the Trigonometric formulas to find both missing sides.

Unfortunately, the Pythagorean Theorem by itself,
will not help you find both of the missing sides.  Remember that you need to know TWO sides of a triangle in order to engage the Pythagorean Theorem.