ANGLE OF ELEVATION AND DEPRESSION and Problem Solving.pptx

Illustrate and solve word problems involving the angle of elevation and angle of depression.

1. ANGLE OF ELEVATION AND DEPRESSION

2. ANGLE OF ELEVATION AND ANGLE OF DEPRESSION Illustrate angles of elevation and angles of depression. Solve real-life problems using the Trigonometric Ratios involving angles of elevation and angles of depression. Objectives:

3. Ө H O SOH S in Ө = O pposite H ypotenuse Ө H A CAH C os Ө = A djacent H ypotenuse Ө A O TOA T a n Ө = O pposite A djacent Give the MNEMONIC/ACRONYM of the 3 Trigonometric ratio.

4. Horizontal line LINE OF SIGHT the imaginary line that connects the eye of an observer to the object being observed. T he horizontal line serves as  the reference line from which the angles of elevation and depression are measured.

5. Line of Sight Angle of Elevation Angle of elevation - t he angle from the horizontal to the line of sight of the observer to the object ABOVE. Horizontal line

6. Line of Sight Angle of Elevation A ngle of elevation is an angle between a horizontal line from the observer and the line of sight to an object that is above the horizontal line.

7. Horizontal line What about if the object is below the horizontal line?

8. Line of Sight Angle of Depression Angle of depression -the angle from the horizontal to the line of sight of the observer to the object BELOW. Horizontal line

9. Line of Sight Angle of Depression Angle of Depression is an angle between a horizontal line from the observer and the line of sight to an object that is below the horizontal line. It is the opposite of angle of elevation. Line of sight is an imaginary line that connects the eye of the observer to the object being observed.

10. Angle of Depression Angle of Elevation Note: The angle of elevation and the angle of depression are equal because of the alternate interior angle of the transversal.

11. QUIZ:

12. QUIZ:

13. ACTIVITY: ELEVATION OR DEPRESSION A boy looking at the flying kite Students singing the National Anthem looking at the raising of the Flag. A man on top of a building observing a car on the road. A Father from the second floor of the building looking at his son on the street. A baby crawling looking at her mother.

14. ACTIVITY: ELEVATION OR DEPRESSION A boy looking at the flying kite Students singing the National Anthem looking at the raising of the Flag. A man on top of a building observing a car on the road. A Father from the second floor of the building looking at his son on the street. A baby crawling looking at her mother. ELEVATION ELEVATION DEPRESSION DEPRESSION ELEVATION

15. Remember to follow the following steps in solving word problems. Step 1 Draw an illustration and label it with the given data. Step 2 Assign a variable for what the problem requires. Step 3 Formulate the applicable trigonometric ratio and solve. Step 4 Check if the solved value satisfies the given condition(s) in the problem. Step 5 State the conclusion/ answer to the problem.

16. Problems on Angle of Elevation

17. Problem #1 1. When the angle of elevation of the sun is 55°, the shadow of a coconut tree is 12 m in length. What is the height of the coconut tree?

18. Solution: Let x be the height of the coconut tree ɵ is shadow of a coconut tree is 12 m in length   12m   x 12m x  

19. Solution: Let x be the height of the coconut tree ɵ is shadow of a coconut tree is 12 m in length   12m x   opp adj tan ɵ =   tan =   x =12 * tan   x =12 * 1.4281 x =17.14m 17.14m

20. Problem #2 2. An ant is 5 m away from the foot of a 10 m high lamp post. Find out the angle made by the ant’s eye with the topmost point of the post. Solution: Let ɵ bangle of elevation 10m the height of the lamp post 5m distance of the ant from the foot of post

21. Solution: Let ɵ bangle of elevation 10m the height of the lamp post 5m distance of the ant from the foot of post opp adj tan ɵ =   tan ɵ =   tan ɵ =   ɵ = ( )   ɵ  

22. Problems on Angle of Depression

23. Example #1: If the angle of depression θ is 30° and the distance of the horizontal line EH is 25 meters, find the length of the vertical line AH.

24. Example #2: How far is the boat from the lighthouse if the lighthouse is 143 meters tall and the angle of depression to the boat is 26°?

25. Example #3: A bamboo pole is leaning against a coconut tree. It makes an angle of depression of 40°. Find the length of the bamboo pole if the distance of the coconut tree from the bottom part of the bamboo pole is 16 ft.

26. Example #4: The distance between the ground and the eyes of the chicken is 28 cm, while the worm is 39 cm away from the chicken. Find the angle of depression when the chicken is looking at the worm on the ground.

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31. Quiz #5:

32. Checking of Quiz

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37. Quiz #5:

38. Thank You