30 - 60 - 90 Triangles And You! Remember the Pythagorean Theorem? The sum of the square of the...
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Transcript of 30 - 60 - 90 Triangles And You! Remember the Pythagorean Theorem? The sum of the square of the...
30- 60- 90 TrianglesAnd You!
Remember the Pythagorean Theorem?
The sum of the square of the legs is equal to the square of the hypotenuse.
a2 + b2 = c2
30
60a
b
c
Solve for the missing side!
a2 + b2 = c2
30
603
b
6 32 + b2 = 62
9 + b2 = 36
b2 = 27
b = 27
b = 3 3
b = 3 3
First we need the Pythagorean Theorem!
Square the numbers!
Substitute the correct values!
Subtract 9 on both sides!
Take the square root on both sides!
Simplify the square root!
That’s a lot of work for one answer!
Wouldn’t it be nice if there was a faster and
shorter way!?!
But where do we start?
30
603
6
3 3
Let’s identify the sides of a 30-60-90 triangle
30
603
6
3 3
Hypotenuse The longest side located across the right angle!
Let’s identify the sides of a 30-60-90 triangle
30
603
6
3 3
Hypotenuse
Long LegThe side located across the 60 angle!
Let’s identify the sides of a 30-60-90 triangle
30
603
6HypotenuseShort Leg
Long Leg
The shortest side located across the 30 angle!
30
603
6HypotenuseShort Leg
Long Leg
It’s very important to remember where the sides are located!!
Let’s look back at the original problem!
30
603
6
3 3
Notice how the hypotenuse is twice as big as the short side!
Hypotenuse = Short Leg x 2Hypotenuse = 3 x 2 Hypotenuse = 6
30
603
6
3 3
Now, compare the short leg with the long leg!
Long Leg = Short leg x 3
Long Leg = 3 x 3
Long Leg = 3 3
Notice how the long leg equals the short leg multiply by the square root of three!
30
603Short Leg
So, if you know the value of the short leg, then you can figure out the
other two sides!
Hypotenuse = Short Leg x 2
Long Leg = Short leg x 3
Let’s try a couple of problems!
30
607
c
b
Short Leg = 7
Hypotenuse = Short Leg x 2
Hypotenuse = 7 x 2Hypotenuse = 14
Long Leg = Short leg x 3
Long Leg = 7 x 3
Long Leg = 7 3
Try this one!
30
609
c
b
Short Leg = 9
Hypotenuse = Short Leg x 2
Hypotenuse = 9 x 2Hypotenuse = 18
Long Leg = Short leg x 3
Long Leg = 9 x 3
Long Leg = 9 3
30
603Short Leg
Remember, the following formulas only occur in a 30-60-90 triangle!
Hypotenuse = Short Leg x 2
Long Leg = Short leg x 3
THE END!
