30 60-90 triangles

1. Special Right Triangles 30 – 60 – 90 Triangles

2. Special Right Triangles Directions As you view this presentation, take notes and work out the practice problems. When you get to the practice problem screens, complete the step in your notebook before continuing to the next slide.

3. 30- 60- 90 Triangles l s 30 o 60 o h In a 30 – 60 – 90 triangle, the side across from the 30 o angle is the short side and often labeled s. In a 30 – 60 – 90 triangle, the side across from the 60 o angle is the long side and often labeled l. The hypotenuse is often labeled h.

4. 30- 60- 90 Triangles Understanding the Shortcuts s 30 o 60 o h l To understand the relationship between the short side and the hypotenuse, draw a second 30 - 60 – 90 triangle with the same dimensions as the original triangle. Arrange the triangles to form an equilateral triangle with side l as the common side.

5. 30- 60- 90 Triangles Understanding the Shortcut for Finding the Length of the Hypotenuse s 30 o 60 o h l h s Because the triangle is an equilateral triangle, s + s = h or 2s = h

6. 30- 60- 90 Triangles Understanding the Shortcut for Finding the Length of the Long Leg s 30 o 60 o h = 2s l h s The Pythagorean Theorem is used to show the relationship between the long side, l, the short side, s, and the hypotenuse, h. s 2 + l 2 = h 2 s 2 + l 2 = (2s) 2 l 2 = 4s 2 – s 2 l 2 = 3s 2 = l = s  

7. 30- 60- 90 Triangles Using the Shortcuts when s is Known s 30 o 60 o h = 2s l = s   When the Short Side is known: Short side = s Long side = s Hypotenuse = 2s  

8. 30- 60- 90 Triangles Practice Problem 1 s = 5 30 o 60 o Finding the lengths of the hypotenuse and long side when s = 5 l = ? h= ?

9. 30- 60- 90 Triangles Practice Problem 1 s = 5 30 o 60 o h = 2s l = s   Finding the lengths of the hypotenuse and long side when s = 5 Remember the shortcuts

10. 30- 60- 90 Triangles Practice Problem 1 30 o 60 o h = 10 l = 5   l = s = 5 h = 2s = 2* 5 = 10   Finding the lengths of the hypotenuse and long side s = 5 Remember the shortcuts s = 5

11. 30- 60- 90 Triangles Using the Shortcuts when l is Known s =   30 o 60 o h =   l Long Side = l Short Side l = s l/ = s / = s   Hypotenuse h = 2s OR h = 2( ) h =  

12. 30- 60- 90 Triangles Practice Problem 2 30 o 60 o Finding the lengths of the hypotenuse and short side when l = 7 l = 7 h = ? s = ?

13. 30- 60- 90 Triangles Practice Problem 2 30 o 60 o Finding the lengths of the hypotenuse and short side when l = 7 Remember the shortcuts l = 7 s =   h = 2s = =  

14. 30- 60- 90 Triangles Practice Problem 2 30 o 60 o Finding the lengths of the hypotenuse and short side when l = 7 Remember the shortcuts s = = h = 2s = 2( )=   l = 7 s =   h =  

15. 30- 60- 90 Triangles Using the Shortcuts when h is Known s = h/2 30 o 60 o h l =   Hypotenuse = h Short Side h = 2s h/2 = 2s/2 h/2 = s Long Side l = s OR l = (h/2)  

16. 30- 60- 90 Triangles Practice Problem 3 30 o 60 o Finding the lengths of the short side and the long side when h = 1 h = 1 s = ? l = ?

17. s = h/2 30 o 60 o h = 1 l =   Finding the lengths of the short side and the long side when h = 1 Remember the shortcuts 30- 60- 90 Triangles Practice Problem 3

18. s =   30 o 60 o h = 1 l =   Finding the lengths of the short side and the long side when h = 1 Remember the shortcuts s = = l = s = ( =   30- 60- 90 Triangles Practice Problem 3

19. s =   30 o 60 o h = 1 l =   In the Unit Circle: h = 1 So remembering these shortcuts for the 30 – 60 – 90 triangle will save you time and work. s = l =   30- 60- 90 Triangles in the Unit Circle