National Math Program Week One Day One (PPT)

A PowerPoint presentation for National Math Program Grade 10 for day 1 week 1.

1. SIN H O A θ TRIGONOMETRY Finding missing sides of a triangle TAN COS

2. LEARNING OUTCOMES Illustrate the Law of Sines a. one side & two angles b. two sides and an angle opposite to the side given Define and describe oblique triangles

3. A right triangle is a triangle with one right angle. A B C b c a 90°

4. Choosing the Trigonometric Ratio

5. Choosing the Trigonometric Ratio

6. O__I__E TRIANGLES

7. OBLIQUE An oblique triangle is any triangle that is not a right triangle. TRIANGLES

8. Triangles with one right angle are called __________. Triangles that are not right triangles are called ______________. right triangles. oblique triangles.

9. Calculate your answer HORIZONTAL (LEVEL OF EYE SIGHT)

10. Calculate your answer HORIZONTAL (LEVEL OF EYE SIGHT) It is where the angle goes “upward” from the horizontal. ANGLE OF ELEVATION

11. Calculate your answer HORIZONTAL (LEVEL OF EYE SIGHT) ANGLE OF DEPRESSION It is where the angle goes “downward” from the horizontal.

12. Two airport traffic control towers are 8 km apart. An airplane is flying over in between two towers. The pilot determines that the angle of depressions of the airplane to tower A and B are 40° and 47° respectively. Using the illustration, how will you find the distance of the airplane from tower A?

13. A B 8 km 40° 47° ?

14. Case 1: Given the measurements of two angles and its included side. ASA (Angle – Side – Angle

15. Case 1: ASA (Angle – Side – Angle

16. Case 1: ASA (Angle – Side – Angle

17. Case 2: Given the measurements of two angles and a side not in between them. SAA (Side – Angle – Angle

18. Case 2: SAA (Side – Angle – Angle

19. Case 2: SAA (Side – Angle – Angle

20. Case 3: Given the measurements of two sides and an angle not included in the known side. SSA /ASS (Side – Side – Angle

21. Case 3: SSA /ASS (Side – Side – Angle

22. LAW of This law states that the ratio of the sine of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of sine of other angle to its opposite side; any pair of proportions may be used to solve for a missing angle or side. SINES

23. LAW of SINES

24. Calculate your answer

25. Calculate your answer

26. Calculate your answer

27. Calculate your answer

28. Calculate your answer Given Δ𝐴𝐵𝐶, 5. 𝑐 = 22,𝑚∠𝐵 = 135°, 𝑎 = 31

29. 1. Define oblique triangles. 2. How to solve an oblique triangles? 3. Can you give one theorem or law that can be used to solve an oblique triangles? 4. Define Law of Sines.

30. Calculate your answer

31. Calculate your answer

32. Calculate your answer

33. Calculate your answer

34. Calculate your answer Given Δ𝐴𝐵𝐶, 5. 𝑐 = 42 ,𝑚∠𝐵 = 125°, 𝑎 = 16