GRADE 9 MATH PRESENTATION.pptx

Mathematics

1. For our agreement and online rules CTIVELY PARTICIPATE & ALWAYS TRY BEST E RESPECTFUL AT ALL TIMES LICK HAND RAISE BUTTON IF YOU HAVE A QUESTION

2. HAPPY EXCITED 1 2

3. A NGLES OF E LEVATION AND A NGLES OF D EPRESSION

4. A ngle of E levation The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal.

5. Example

6. A ngle of Depression The term angle of depression denotes the angle from the horizontal down ward to an object. An observer’s line of sight would be below the horizontal.

7. Example

8. Line of Sight L ine of sight is an imaginary line that connects the eye of an observer to the object being observed.

9. Example

10. Definition of Terms Hypotenuse is the longest side of a triangle. It is also the side opposite from the right angle (90˚) results in different outcomes. Opposite is the one across from a given angle.

11. Adjacent is adjacent (next to) to the angle θ. In a right-angled triangle it is the side between the angle θ and the right angle.

12. Example

13. Problem 1 A nursery plants a new tree and attaches a guy wire to help support the tree while its roots take hold. An eight-feet wire is attached to the tree and to a stake in the ground. From the stake in the ground the angle of elevation of the connection with the tree is 42˚. Find to the nearest tenth of feet, the height of the connection point on the tree.

14. Figure 1

15. Solution 1 This problem deals with “opposite” and “hypotenuse” making it a sine problem. sinθ = sin42˚ = 8sin45˚ = x x = 5.4 feet  

16. Problem 2 The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60˚. Find the height of the building.

17. Figure 2

18. Solution 2 Now we need to find the length of the side AB. tanθ = tan60˚ = tan60˚ = 50tan60˚ = AB AB = 1.732m  

19. Problem 3 A man wants to determine the height of a wall. A ladder is learning against a vertical wall makes an angle of 20˚ with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder.

20. Figure 3

21. Solution 3 Now we need to find the length of the ladder (AC). cosθ = cos20˚ = cos20˚ = 3cos20˚ = BC BC = 3.192  

22. Thank you for listening Have a great day everyone

23. ASSIGNMENT Check and review your answers in your modules, and prepare yourself next meeting for our continuation of our discussion and I will call one by one to answer.