30 60 90 Triangles

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30?- 60?- 90? Triangles

• And You!

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Remember the Pythagorean Theorem?

• The sum of the square of the legs is equal to the
  square of the hypotenuse.

a2 b2 c2
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Solve for the missing side!
First we need the Pythagorean Theorem!
a2 b2 c2
Substitute the correct values!
 32 b2 62
Square the numbers!
9 b2 36
Subtract 9 on both sides!
b2 27
Take the square root on both sides!
Simplify the square root!
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Thats a lot of work for one answer!
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Wouldnt it be nice if there was a faster and
shorter way!?!
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But where do we start?
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Lets identify the sides of a 30?-60?-90? triangle
The longest side located across the right angle!
Hypotenuse
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Lets identify the sides of a 30?-60?-90? triangle
Hypotenuse
Long Leg
The side located across the 60? angle!
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Lets identify the sides of a 30?-60?-90? triangle
Hypotenuse
Short Leg
The shortest side located across the 30? angle!
Long Leg
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Its very important to remember where the sides
are located!!
Hypotenuse
Short Leg
Long Leg
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Lets look back at the original problem!
Notice how the hypotenuse is twice as big as the
short side!
Hypotenuse Short Leg x 2
Hypotenuse 3 x 2
Hypotenuse 6
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Now, compare the short leg with the long leg!
Notice how the long leg equals the short leg
multiply by the square root of three!
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So, if you know the value of the short leg, then
you can figure out the other two sides!
60?
Hypotenuse Short Leg x 2
3
Short Leg
30?
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Lets try a couple of problems!
Short Leg
7
Hypotenuse Short Leg x 2
Hypotenuse 7 x 2
Hypotenuse 14
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Try this one!
Short Leg
9
Hypotenuse Short Leg x 2
Hypotenuse 9 x 2
Hypotenuse 18
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Remember, the following formulas only occur in a
30?-60?-90? triangle!
60?
Hypotenuse Short Leg x 2
3
Short Leg
30?
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THE END!
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