1. 7.4 Special Right
Triangles f g u i l b e r t

2. Since base anlge‘s are = opposite sides are =. The triangle is
isosceles.
450 X
450 f g u i l b e r t X

3. 45 - 45 - 90 triangle The hypotenuse is X 450 X X 450 X t f g u i l b

4. 45 - 45 - 90 triangle X2 + X2 = c2 X√2 c 2X2 = c2 X ____ ___
____ ___
√2 X2 = √ c2
√2 X = c c
X√2 X X f g u i l b e r t

5. ex 1 Given the short side is 5 find the hypotenuse. 450 5 5 450 5 t fl b e r t 5

6. ex 2 Given the hypotenuse, Find the legs. 9 √2 450 √2 9 9 450 9 t f gb e r t 9

7. ex 3 Find the legs. 7 √2 450 √2 7 7 √2 7√2 2 450 7 simplified form √2u i l b e r t 7 √2

8. 30 - 60 - 90 triangle The shortest side is opposite 300. 600 X 300 t fu i l b e r t

9. Longest side is opposite 900 . It is double the short side. 300 2X
triangle
Longest side is opposite
900 . It is double
the short side.
300 2X
600 f g u i l b e r t X

10. 30 - 60 - 90 triangle The medium side is opposite 600 . It is X√3 .
300 2X
X√3
600 f g u i l b e r t X

11. ex 4 Find the other sides. 300 Hypotenuse is (2)(8). 16 600 8 t f g ul b e r t 8

12. ex 4
300
Medium side
is (8)(√3). 16
8√3
600 f g u i l b e r t 8

13. Looks like a
30 degree angle ! f g u i l b e r t

14. ex 5 Find the other sides. 300 Short side is 10 half of 10. 600 5 t fg u i l b e r t 5

15. ex 5
300
Medium side
is 5 √3. 10
5√3
600 f g u i l b e r t 5

16. ex 6 Find the other sides. You have the medium side x√3. 600 300 2√3 tg u i l b e r t
2√3

17. ex 6
Short side is X.
2√3 √3
= 2
600 2
300 f g u i l b e r t
2√3

18. ex 6 Double the short side to find the hypotenuse. 600 4 2 300 2√3 t fg u i l b e r t
2√3

19. ex 7 Short side is √3 √3 600 Double to get 2√3 hypotenuse. 300 t f g u

20. ex 7 Short side is √3 √3 600 3 To get medium side 2√3
multiply short by √3.
(√3 )(√3 ) = 3
2√3
300 f g u i l b e r t

21. short side by √3 knucklehead.
In a multiply the
short side by √3 knucklehead. f g u i l b e r t

22.
45o
x√2 X
300 2X
45o
x√3 X
600 f g u i l b e r t X

23. Find the Area A = 1/2 b h ∆ is equilateral so all sides = 8 8 8 8 t fg u i l b e r t 8

24. A = 1/2 b h ∆ is equilateral so all angles = 600 8 8 8 600 600 600 t f

25. A = 1/2 b h How can you use 30-60-90 to find height ? 8 8 8 600 600l b e r t
600
600 8

26. A = 1/2 b h How can you use 30-60-90 to find height ? 8 h 300 600 t fl b e r t
600

27. A = 1/2 b h Short side is 4. h = 4√3 8 4√3 Find area. 4 300 600 t f gu i l b e r t
600 4

28. A = 1/2 b h
= 1/2 (8)(4√3)
h = 16√3
300 8
4√3 f g u i l b e r t
600 4

29. thought for the day
No man is
an island
John Donne f g u i l b e r t