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30 - 60  - 90  Triangles

30 - 60  - 90  Triangles. And You!. 60 . c. a. 30 . b. 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. 60 . 6. 3. 30 . b = 3 3. b = 3 3. b. b = 27. Solve for the missing side!.

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30 - 60  - 90  Triangles

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  1. 30- 60- 90 Triangles And You!

  2. 60 c a 30 b Remember the Pythagorean Theorem? The sum of the square of the legs is equal to the square of the hypotenuse. a2 + b2 = c2

  3. 60 6 3 30 b = 3 3 b = 3 3 b b = 27 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!

  4. That’s a lot of work for one answer!

  5. Wouldn’t it be nice if there was a faster and shorter way!?!

  6. 60 6 3 30 3 3 But where do we start?

  7. 60 6 3 30 3 3 Let’s identify the sides of a 30-60-90 triangle The longest side located across the right angle! Hypotenuse

  8. 60 6 3 30 3 3 Let’s identify the sides of a 30-60-90 triangle Hypotenuse Long Leg The side located across the 60 angle!

  9. 60 6 3 30 Let’s identify the sides of a 30-60-90 triangle Hypotenuse Short Leg The shortest side located across the 30 angle! Long Leg

  10. 60 6 3 30 It’s very important to remember where the sides are located!! Hypotenuse Short Leg Long Leg

  11. 60 6 3 30 3 3 Let’s 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

  12. 60 6 Long Leg = Short legx3 3 Long Leg = 3x3 Long Leg =3 3 30 3 3 Notice how the long leg equals the short leg multiply by the square root of three! Now, compare the short leg with the long leg!

  13. Long Leg = Short legx3 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 Short Leg 3 30

  14. 60 c 7 30 Long Leg =Short legx 3 b Long Leg=7x 3 Long Leg = 7 3 Let’s try a couple of problems! Short Leg = 7 Hypotenuse =Short Leg x 2 Hypotenuse = 7 x 2 Hypotenuse = 14

  15. 60 c 9 30 Long Leg =Short legx 3 b Long Leg=9x 3 Long Leg = 9 3 Try this one! Short Leg = 9 Hypotenuse =Short Leg x 2 Hypotenuse = 9 x 2 Hypotenuse = 18

  16. Long Leg = Short legx3 Remember, the following formulas only occur in a 30-60-90 triangle! 60 Hypotenuse =Short Leg x 2 Short Leg 3 30

  17. THE END!

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