1. Trigonometry: Part 1 Similarity ReviewMenu This is the type of problem from 1 st semester.. We used the measurements in one triangle to find the measurements in a similar triangle. NEXT….

2. Trigonometry: Part 1 Similarity ReviewMenu Now we are going to do this when we only have 1 triangle

3. So now, you are going to see problems where… …you have 1 triangle with missing measurements … you will draw a similar triangle & measure it to solve the problem

4. These are all problems that involve a 20-70-90 triangle. To solve them, we need to know what a 20-70-90 triangle is supposed to measure. To solve them, we need to know what a 20-70-90 triangle is supposed to measure.

5. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu EXAMPLE PROBLREM:

6. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu Using what we know about similar triangles, we can make indirect measurements. For example, we can calculate the actual height of the lights in this picture without going to the location to measure them.

7. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu Each lightpost is at the goal line 300 feet apart X ft

8. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu Each lightpost is at the goal line 300 feet apart 300ft X ft We know this because all football fields are 300 ft (100 yards) long

9. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu We can create a triangle 300ft X ft

10. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu And measure the angles with a protractor 300ft X ft 20 0 We assume the lightpost makes a 90 0 angle with the ground because it would fall over if it didn’t

11. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu Next, we are going to figure out how tall the light is (X) by creating a similar triangle on your paper. 300ft X ft 20 0 70 0 You are going to create a 20-70-90 triangle, and we will use proportions to find X.

12. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle You are going to create a 20-70-90 triangle, and we will use proportions to find X.

13. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle Use a ruler to draw segment AB. Make it as long as you want AB10cm

14. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle Use a protractor to create a 20 0 angle at point B AB10cm

15. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0

16. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 Use a protractor to create a 90 0 angle at point A

17. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0

18. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C Complete the triangle with point C

19. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C Use a ruler to measure AC ????cm

20. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C AND the hypotenuse ????cm

21. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C We are going to use the 20 0 as our reference angle We could pick the 70 instead if we wanted.

22. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C From the 20 0, label your sides O, A and H

23. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C Add and complete this table on your paper From a 20 0 angle:

24. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu In your note packet, on page 3, draw a 20-70-90 triangle AB10cm 20 0 C From a 20 0 angle: Make sure to compare your answers to other students or check with the teacher if necessary. If you have these wrong, all the other problems will be wrong too.

25. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu Now you are going to use the triangle you drew for 5-1 to answer a series of problems about similar (20-70-90) triangles

26. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Now your triangle 5-1 should be similar to this triangle.

27. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Using the 20 0 as your reference angle, label the 3 sides O, A and H

28. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Which is the side you are trying to find? (O, A or H)?

29. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Which is the side you already know? (O, A or H)?

30. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Hopefully, you identified the side you are trying to find  O The side you know  A Look at the ratios you created in 5-1. One of them involves O and A:

31. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Hopefully, you identified the side you are trying to find  O The side you know  A Look at the ratios you created in 5-1. One of them involves O and A: If you measured perfectly, you would have gotten 0.36 for O/A

32. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Hopefully, you identified the side you are trying to find  O The side you know  A Look at the ratios you created in 5-1. One of them involves O and A: Use your own number to see how close you would be on your own.

33. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 300ft X ft 20 0 70 0 Now solve this equation for X!

34. The actual answer for how high the light post is : 108ft If your numbers for O, A and H are bad… use these instead: From a 20 0 angle: If you measured perfectly, these are the numbers you would get

35. Now solve these problems in your note packet the same way: Check your answers with your teacher before you move on to the next page.

36. All the problems you did on page 4 used a 20-70-90 triangle Now, we are going to switch to problems that use a 40-50-90

37. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 We are going to solve problems involving a 40-50-90 triangle. First we need to know what a 40-50-90 is supposed to measure. So…Draw a 40-50-90 triangle: (use the exact same directions we did for the 20-70-90, just when you get to the point where you are going to draw a 20 0 angle, make it 40 0 instead.) Measure the sides. Find the ratios, fill in the table. Compare your answers with others (or check with your teacher) to make sure they are right. Use these ratios to answer the remaining problems on the page.

38. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 Step 1Draw a 40-50-90 triangle Follow the same directions you used to draw the 20-70-90 on page 3

39. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 Step 1Draw a 40-50-90 triangle Step 2Get a ruler and measure the three sides.

40. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 Step 1Draw a 40-50-90 triangle Step 2Get a ruler and measure the three sides. Step 3 Draw in and complete this table (we will use the 40 0 as our reference angle) From a 40 0 angle:

41. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 Step 1Draw a 40-50-90 triangle Step 2Get a ruler and measure the three sides. Step 3 Draw in and complete this table (we will use the 40 0 as our reference angle) Step 4 Compare your ratios from the table with classmates to make sure they are correct

42. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu 5-2 Step 1Draw a 40-50-90 triangle Step 2Get a ruler and measure the three sides. Step 3 Draw in and complete this table (we will use the 40 0 as our reference angle) Step 4 Compare your ratios from the table with classmates to make sure they are correct Step 5 Use your table to find X in the problems on the bottom of the page.

43. Trigonometry: Part 5Solving Problems with Similar TrianglesMenu You don’t have to draw a triangle for each problem. All you need are the ratios: You can find them on page 6 in your note packet.

44. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Use the ratios on page 6 of your note packet to answer the problems in section 6. Pages 7-8 in your note packet Part 6

45. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu This is an actual photo (not really) of Godzilla at the Kiyomo bridge outside Hokaido, Japan. We know that the bridge is exactly 1,234 ft long. Find the height of the misunderstood monster.

46. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu 30 0 1234ft This is an actual photo (not really) of Godzilla at the Kiyomo bridge outside Hokaido, Japan. We know that the bridge is exactly 1,234 ft long. Find the height of the misunderstood monster.

47. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu We describe this picture without seeing it by using the phrase “ANGLE OF ELEVATION” Angle of elevation means “What angle you have to look up at something to see it”

48. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Godzilla is 1234 ft away. The angle of elevation to the top of his head is 30 0. How tall is Godzilla?

49. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Find the height of the giraffe. Student drawing

50. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Student drawing Joe is flying a kite. The kite gets really high up. So high, he has run out of his 1,000 ft spool of string. He wants to know how high up his kite got, so he measures the angle of elevation to the kite, and gets 45 degrees. How high up is the kite? 45 0

51. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Student drawing Find the height of “the thing from planet X”.

52. Trigonometry: Part 6Solving Problems with Similar TrianglesMenu Complete part 6 (pages 7, 8 in your note packet) Use the ratios on page 6 to solve the problems Compare your answers with another student to check if you are doing them right

53. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. Help for the first 2 problems on page 8

54. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. Which side do we know (O,A or H)? Which side do we want to know? Help for the first 2 problems on page 8

55. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O Which side do we know (O,A or H)? Which side do we want to know? Help for the first 2 problems on page 8

56. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What kind of triangle is it? Help for the first 2 problems on page 8

57. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What kind of triangle is it? 30-60-90 Help for the first 2 problems on page 8

58. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What kind of triangle is it? 30-60-90 What is O/H supposed to be for a 30 0 angle? (look on page 4) Help for the first 2 problems on page 8

59. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What kind of triangle is it? 30-60-90 What is O/H supposed to be for a 30 0 angle? (look on page 4) 0.50 Help for the first 2 problems on page 8

60. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What kind of triangle is it? 30-60-90 What is O/H supposed to be for a 30 0 angle? (look on page 4) 0.50 Help for the first 2 problems on page 8

61. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O What is O/H supposed to be for a 30 0 angle? (look on page 4) 0.50 The sides we are using Their measurements in the triangle What it should be equal to. Help for the first 2 problems on page 8

62. Trigonometry: Part 6Using Similar TrianglesMenu Now we are going to use the triangles you have drawn to answer the problems on page 6. H O Help for the first 2 problems on page 8

63. Trigonometry: Part 6Using Similar TrianglesMenu Help for the first 2 problems on page 8

64. Trigonometry: Part 6Using Similar TrianglesMenu A O Help for the first 2 problems on page 8

65. Trigonometry: Part 6Using Similar TrianglesMenu A O Help for the first 2 problems on page 8

66. Trigonometry: Part 6Using Similar TrianglesMenu A O Help for the first 2 problems on page 8