Angle of Elevation and Depression_4THQ_COT.pptx

Angle of Elevation and Depression_4THQ_COT.pptx

1. REVIEW!

2. GROUP ACTIVITY MOTIVATION You will be group into four groups . Each group will choose their leader and a secretary. You will be given two pictures, a marker and manila paper. List five differences of the two pictures you have and write it on the manila paper. You are given five minutes to finish the activity and present their work to the class.

3. How did you know that the person is sad? 01 02 W hat are the other things that you have noticed in the activity? 03 Where do negative and positive emotions lead a person? 04 Follow up Questions How did you know that the person is happy?

4. Angles of Elevation and Depression Quarter 4 - Week 3

5. 1. Illustrates angles of elevation and angles of depression. (M9GE-IVd -1) Learning Competencies 2. U ses trigonometric ratios to solve real-life problems involving right triangles.

6. EXAMPLE PROBLEM 1: An observer looks up at an angle of 45 o looking at the top of a tower. The tower is 300ft away measured along the ground. What is the height of the tower? 300 ft   h

7. EXAMPLE PROBLEM 2:

8. EXAMPLE PROBLEM 3:

9. EXAMPLE PROBLEM 4: A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

10. EXAMPLE PROBLEM 6:

11. Solve Me! 1. At a point on the ground 50 ft. from the front of a tree the angle of elevation to the top of the tree is . Find the height of the tree.   2. A ladder is leaning against a wall. The foot of the ladder is 6 ft. from the wall. The ladder makes an angle of with the level ground. How high on the wall does the ladder reach?  

12. Solve Me! 3. A wooden ladder 24ft long leans against a wall and makes an angle of How high up to the wall does the wooden ladder reach?   4. A 20-foot ladder leans against a building and makes angle of with the ground. Find the distance between the foot of the ladder and the building.  

13. EXAMPLE PROBLEM 5:

14. Special Acute Angle 2 1 1 2 2 1 1 2

15. EXAMPLE PROBLEM 1: An observer looks up at an angle of 45 o looking at the top of a tower. The tower is 300ft away measured along the ground. What is the height of the tower? 300 ft   h Given: Angle of elevation is   Distance of the tower from observer is 300 ft . Let h represents the height of the tower. Equation of the Problem:  

16. UNLOCKING TERMS HORIZONTAL LINE It is a straight horizontal line that comes from the eye of the observer. LINE OF SIGHT It is straight line drawn from the eye of the observer to the point or object being viewed. ANGLE OF ELEVATION I t is an angle formed between the horizontal line and the line of sight ABOVE the horizontal line. ANGLE OF DEPRESSION Horizontal line Line of sight Line of sight It is an angle formed between the horizontal line and the light of sight BELOW the horizontal line. Angle of Elevation Angle of Depression

17. The Steps in Solving Angles of Elevation and Depression 1. Analyze the problem. 2. Illustrate/draw the figure. 3. Identify the missing part of a right triangle. 4. Identify the trigonometric ratios/functions to be used. 5. Solve the problem.

18. EXAMPLE PROBLEM 1: The angle of depression from a lamp post to a point on the ground is . How long is the light beam to the nearest whole number if the lamp post is 10 m high?   10 m    

19. EXAMPLE PROBLEM 2: The angle of depression from a lamp post to a point on the ground is . How long is the light beam to the nearest whole number if the lamp post is 10 m high?   10 m   Given: Height of lamp post is 10 m . The angle if depression from the lamp post to the point is .   Let x represents the distance of the light beam.   Equation of the Problem:   Solution 1:

20. EXAMPLE PROBLEM 2: The angle of depression from a lamp post to a point on the ground is . How long is the light beam to the nearest whole number if the lamp post is 10 m high?   10 m   Given: Height of lamp post is 10 m . The angle if depression from the lamp post to the point is .   Let x represents the distance of the light beam.   Equation of the Problem:   Solution 2:

21. EXAMPLE PROBLEM 3: An airplane is flying at a height of 5 km above the ground. The distance along the ground from the airplane to the airport is 8 km. what is the angle of depression from the airplane to the airport? Our notation for degrees is θ 8 km 5 km  

22. EXAMPLE PROBLEM 3: An airplane is flying at a height of 5 km above the ground. The distance along the ground from the airplane to the airport is 8 km. what is the angle of depression from the airplane to the airport? Our notation for degrees is θ 8 km 5 km   Given: Height of airplane flying above the ground is 5 km . The distance along the ground from the airplane to the airport is 8km . Equation of the Problem:   Let represents the angle of depression from the airplane to the airport.  

23. ACTIVITY! DRAW MY PROBLEM Directions: 1. Draw the pictures presented by the information in the problems given. 2. Assume that buildings, ladders, etc. are all on level ground. 3. Clear, neat and accurate illustrations are necessary. 4. Solve the problems. *Show your complete solution

24. Assignment To measure the amplitude of an angle, a measuring instrument called a protractor is needed. The protractor has degrees, can be circular or semicircular and is usually made of plastic

25. Null It's the angle that is 0° Acute It’s smaller than 90º Straight It's the angle that is 180º Reflex It’s more than 180° Right It's the angle that is 90° Full rotation It's the angle that is 360° Types of angles based on measurement Obtuse Between 90° and 180°

26. They both add up to 180º They both add up to 90º Types of angle pairs Supplementary angles Complementary angles

27. Angles according to their position Consecutive angles Adjacent angles Opposite angles Angles that share a side and vertex They are consecutive angles and the side they do not share is part of the same straight line They are angles that share the vertex but none of the sides

28. The protractor To measure the amplitude of an angle, a measuring instrument called a protractor is needed. The protractor has degrees, can be circular or semicircular and is usually made of plastic

29. Steps to measure an angle 1 The center of the protractor, which is usually indicated by a line, should be placed at the vertex of the angle (the origin of the angle) 3 The graduation of the remaining side is marked on the protractor and this is the amplitude 2 Then check that one of the sides of the angle coincides with the base of the protractor

30. Activities 04

31. Exercise 1 Circle the right angles with these circles

32. Exercise 2 : angle vocabulary It is the one that is between 90° and 180° Angles that add up to 90° Angle measuring instrument An angle with 180° Angles that share the vertex, but not the sides It is the one that has 0° Angles that add up to 180° They are angles that share a side and the vertex It is the portion of the plane between two straight lines with a common origin called vertex It is the angle with 360º 1 2 3 4 5 6 7 8 9 10

33. Exercise 3 Draw the following angles A right angle Two acute angles Three obtuse angles

34. Exercise 4 Say the name of the angle according to the classification according to its measurement

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