30  - 60  - 90  Triangles And You! Remember the Pythagorean Theorem? The sum of the square of the legs is equal to the square of the hypotenuse. a.

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Presentation transcript:

30  - 60  - 90  Triangles And You!

Remember the Pythagorean Theorem? The sum of the square of the legs is equal to the square of the hypotenuse. a 2 + b 2 = c 2 30  60  a b c

Solve for the missing side! a 2 + b 2 = c 2 30  60  3 b b 2 = b 2 = 36 b 2 = 27 b = 27 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  60  3 6 3

Let’s identify the sides of a 30  -60  -90  triangle 30  60  Hypotenuse The longest side located across the right angle!

Let’s identify the sides of a 30  -60  -90  triangle 30  60  Hypotenuse Long Leg The side located across the 60  angle!

Let’s identify the sides of a 30  -60  -90  triangle 30  60  3 6 Hypotenuse Short Leg Long Leg The shortest side located across the 30  angle!

30  60  3 6 Hypotenuse Short Leg Long Leg It’s very important to remember where the sides are located!!

Let’s look back at the original problem! 30  60  Notice how the hypotenuse is twice as big as the short side! Hypotenuse = Short Leg x 2 Hypotenuse = 3 x 2 Hypotenuse = 6

30  60  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  60  3 Short 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  60  7 c b Short Leg = 7 Hypotenuse = Short Leg x 2 Hypotenuse = 7 x 2 Hypotenuse = 14 Long Leg = Short leg x 3 Long Leg = 7 x 3 Long Leg = 7 3

Try this one! 30  60  9 c b Short Leg = 9 Hypotenuse = Short Leg x 2 Hypotenuse = 9 x 2 Hypotenuse = 18 Long Leg = Short leg x 3 Long Leg = 9 x 3 Long Leg = 9 3

30  60  3 Short 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!