1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT? Standards 15, 18, 19 END SHOW PRESENTATION CREATED BY SIMON.

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RATIOS IN RIGHT TRIANGLES

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Presentation transcript:

1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT? Standards 15, 18, 19 END SHOW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

2 Standard 15: Students use the pythagoream theorem to determine distance and find missing lengths of sides of right triangles. Los estudiantes usan el teorema de Pitágoras para determinar distancia y encontrar las longitudes de los lados de teoremas rectángulos. Standard 18: Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them, (e.g., tan(x)=sin(x)/cos(x), etc.) Los estudiantes conocen las definiciones de las funciones básicas trigonométricas definidas para los ángulos de triángulos rectángulos. Ellos también conocen y son capaces de usar relaciones básicas entre ellos. (ej., tan(x)=sin(x)/cos(x), etc.) Standard 19: Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. Los estudiantes usan funciones trigonométricas para resolver para una longitud desconocida de un triángulo rectángulo, dado un ángulo y la longitud de un lado. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

6 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

7 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

8 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

9 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

10 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

11 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

12 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13 ADJACENT SIDE HYPOTENUSE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14 OPPOSITE SIDE Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

15 b a c C B A The ADJACENT side to A is side “b” or CA Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

16 b a c C B A The OPPOSITE side to A is side “a” or BC Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

17 k m l L K M What is the adjacent side to M? The ADJACENT side to M is side “k” or LM Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

18 What is the opposite side to M? The OPPOSITE side to M is side “ m ” or KL k m l L K M Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

19 r t s S R T What is the adjacent side to R? The ADJACENT side to R is side “t” or RS Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

20 What is the opposite side to R? The OPPOSITE side to R is side “r” or ST r t s S R T Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

21 z x y Y Z X What is the adjacent side to X? The ADJACENT side to X is side “y” or XZ Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

22 What is the opposite side to X? The OPPOSITE side to X is side “x” or ZY z x y Y Z X Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

23 b a c R Q S What is the adjacent side to S? The ADJACENT side to S is side “b” or RS Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

24 b a c What is the opposite side to S? The OPPOSITE side to S is side “a” or QR R Q S Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

25 o u i C B A What is the adjacent side to C? The ADJACENT side to C is side “o” or CA Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

26 C B A What is the opposite side to C? The OPPOSITE side to C is side “i” or AB o u i Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

27 e i u Q R S What is the adjacent side to Q? The ADJACENT side to Q is side “e” or QS Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

28 What is the opposite side to Q? The OPPOSITE side to Q is side “u” or RS e i u Q R S Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

29 o u i C B A Sin C = Hypotenuse Opposite side SINE u i Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

30 o u i C B A Cos C = Hypotenuse Adjacent side COSINE u o Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

31 o u i C B A Tan C = Adjacent side Opposite side TANGENT i o Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

32 o u i C B A Tan C= i o Adjacent side Opposite side TANGENT Sin C= i u Hypotenuse Opposite side SINE Cos C= o u Hypotenuse COSINE Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

33 b a c C B A Sin A = a Opposite side c Hypotenuse Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

34 b a c C B A Cos A = c Hypotenuse b Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

35 b a c C B A Tan A= a Opposite side Adjacent side b Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

36 b a c C B A Sin B = c Hypotenuse b Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

37 b a c C B A Cos B = c Hypotenuse a Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

38 b a c C B A b Opposite side Adjacent c Tan B = Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

39 k m l L K M Sin M = k Hypotenuse m Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

40 k m l L K M Cos M = k Hypotenuse l Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

41 k m l L K M Tan M= m Opposite side Adjacent l Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

42 k m l L K M Sin L= k Hypotenuse l Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

43 k m l L K M Cos L = k Hypotenuse m Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

44 k m l L K M Tan L = Adjacent m l Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

45 r t s S R T Sin T= s Hypotenuse t Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

46 r t s S R T Cos T= s Hypotenuse r Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

47 r t s S R T Tan T = t Opposite side Adjacent r Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

48 r t s S R T Sin R = s Hypotenuse r Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

49 r t s S R T Cos R = s Hypotenuse t Adjacent side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

50 r t s S R T Tan R = Adjacent t r Opposite side Standard 18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Y Z X Sin Z = 5 Hypotenuse 4 Opposite side Sin Z= 0.8 Standard 18 Find Sin Z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

52 Y Z X Cos Z = 5 Hypotenuse 3 Adjacent side Cos Z= 0.6 Standard 18 Find Cos Z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

53 Y Z X Tan Z = 4 Opposite side Adjacent Tan Z= 1.3 Standard 18 Find Tan Z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved