MATHEMATICS FORM 4

1. MATHEMATICS FORM 4 ANGLES OF ELEVATION AND DEPRESSION

2. Hello there. How are you? Welcome back. Did you know what we are going to learn today? Yes. We are going to learnt about Angles of elevation and depression. However, let’s us recall back what is angle. Do you know angles? If you did not remember about angles, let watch this video together. PLAY VIDEO

3. Now, can you remember what is angles? If yes, good. But today we are going to learn about angles of elevation and depression.

4. INTRODUCTION TO ANGLES OF ELEVATION & DEPRESSION

5. LEARNING Objectives: At the end of the lesson, students will be able to: identify the horizontal line, the angle of elevation and the angle of depression for a particular situation Represent a particular situation involving angles of elevation and depression using diagrams Solve problems involving the angle of elevation and the angle of depression Hi there. Here are our learning objectives for today.

6. Now, first let’s us learn how to identify the horizontal lines, angles of elevation and angles of depression.

7. Horizontal Lines, angles Of elevation & angles Of depression

8. What is angle of elevation? Angle of elevation is the angle between the horizontal line that passes through an observer’s eye and the straight line that joins the observer’s eye to an object situated at the higher lever than the observer. What about the angle of depression? Can you guess it?

9. What is angle of depression? The angle of depression is the angle between the horizontal line that passes through an observer’s eye and the straight line that joins the observer’s eye to an object situated at a lower level than the observer. By the way? Can you tell me what is horizontal line? Now, do you understand what is angle of elevation and angle of depression? If no, let’s us take a look on one diagram…

10. T The diagram on the left shows a tower DQT and a building AB on a horizontal ground. A man at the position R views the peak of the tower T. A ANGLE OF ELEVATION Q R ANGLE OF DEPRESSION B D RQ is the horizontal line The angle of depression of D from R is ∟QRD The angle of elevation of T from R is ∟TRQ

11. Activity 1: Let’s us test your Understanding! QUESTION 1 QUESTION 2

12. QUESTION 1 BACK B P A In the diagram above, AB is a building on a horizontal ground. Identify: The horizontal line The angle of elevation of B from P ANSWER ANSWER

13. NEXT QUESTION 2 T 12.5 m R P 16 m The above diagram shows a vertical pole TP on a horizontal plane. State the horizontal line Find the angle of elevation of T from R ANSWER ANSWER

14. Sssstt…do you really want to know the answer? Well…the answer is : THE HORIZONTAL LINE IS PA. BACK TO QUESTION 1

15. Hmm….the correct answer is : THE ANGLE OF ELEVATION OF B FROM P IS APB BACK TO QUESTION 1

16. The answer is : THE HORIZONTAL LINE IS PR. BACK TO QUESTION 2

17. Well….the correct answer is : THE ANGLE OF ELEVATION OF T FROM R IS TRP BACK TO QUESTION 2

18. Representing a particular situation involving angles of elevation and depression using diagrams

19. You did not know? Don’t worry. I can help you. Here are the steps: Draw the positions of the object and observer Draw the horizontal line Join the eye of the observer and the object Indicate the angle Hi there. Did you know how to represent particular situation involving angles of elevation and depression using diagrams?

20. Do you understand it? Ok..let’s us take a look on one examples ok? Here the example: PQ and RS are two vertical poles on a horizontal plane. These poles are 10m apart. PQ is 9.5m while RS is 5m. The angle of elevation of P from R is 25° and the angle of depression of Q from R is 26°. Draw a labeled diagram to represent this situation. We give you 2 minutes to try to answer it. Ok? Good Luck!

21. P Here are the answer. Check with your answer ok? R 25° 26° Q S

22. How is it? Did your answer correct? Do you want to try one more question ? Try answer this: A vertical pole, TP, with a height of 5m is standing on a horizontal ground PQR. PQR is 10m with PQ=QR. The angle of elevation of vertex T from R is 27° and the angle of elevation of vertex T from Q is 45°. Draw a labeled diagram to represent this situation. CHECK YOUR ANSWER

23. T Here is the correct answer… 45° 27° R P Q How’s your performance? If correct, congratulation! If not, don’t give up. Try again. NEXT

24. Activity 2: handout

25. Hi there. I am Mr. Tiger.. Now we are going to learn the last learning objevtives of Angles of Elevation and Depression topic. We will now learn how to solve problems involving angles of elevation and depression. Let’s go!!

26. Let us take a look on this question: In the diagram below, represent a building BC on a horizontal ground BA. The height of the building is 37m. The angle of depression of A from C is 65°. Calculate the distance BA. C 37m A B

27. Did you know how to solve it? Let us watch this video first and then try to answer the question given earlier. Perhaps this video can help you in order to solve this question. PLAY VIDEO

28. Let us check the answer together: ∟ACB = 90° - 65° = 25° Tan 25° = x / 37 x = 37 tan 25° = 17.25 m # The distance of BA is 17.25 m C D 65° 37m A x m B

29. ACTIVITY 3: QUIZ QUIZ QUESTIONS

30. What have you learnt today? For more information on angles of elevation and depression click here.

31. eXERCISES HOMEWORK

32. The End… PLAY ANGLES GAME click here