AngleofElevation and Depression for Grade 9

Angle of Elevation and Depression topic

2. REVIEWREVIEW
1.What are the common trigonometric ratios that we used in
solvingthe right triangle?
2.When do we use sine?
3.How about the cosine and tangent?

3. REVIEWREVIEW
1.What are the common trigonometric ratios that we
used in solvingthe right triangle?
*We used Sine, Cosine, and Tangent trigonometric
ratios in the right triangle.
2.When do we use sine?
When the opposite side and the hypotenuse is given.
3.How about the cosine and tangent?
When the adjacent side and hypotenuse is given and
for tangent
is when both legs of the triangles are given.

4. Activity: 4 pic 1 word
Direction: You are going to have 4 Pics 1 Word in
order to know what is our lesson for today.

5. 4 pic 1 word
Answer:_____

6. Answer:
_________

7. Answer:
_________

8. Learning Objectives:
*Differentiate the concept of the angle of
depression and angle of elevation;
*Apply sine, cosine and tangent ratios to find
angles of elevation and depression;
*Link the concept of angle of elevation and
depression in real life.

9. “UNLOCKING OF DIFFICULTY”“UNLOCKING OF DIFFICULTY”
What is Line of sigth?

10. LINE OF SIGHT
Is an imaginary line that connects the eye of an
observer to the object being observed.

11. What is the angle of elevation?

12. ANGLE OF ELEVATION
-Is the angle from the horizontal line of the sight
of the observer to the object above.

13. What is the angle of depression?

14. ANGLE OF DEPRESSION
-Is the angle from the line of the sight of the
observer to the object below.
~

15. Try this:
Tony is watching the stars.1.
Anna is looking into 10ft. building.2.
Fiona is looking at her cat.3.

16. Trigonometric function can be used to calculate
distances by finding an angle determined by a
horizontal (x distance) and a line of sight
(hypothenuse).

17. Trigonometric function
SOH-CAH-TOA
sin θ= opp
hyp
cos θ=adj
hyp
tan θ=opp
hyp

18. Skills # 1
Let’s have an example for angle of elevation.
From a point on the ground 47 feet from the
foot of a tree, the angle of elevation of the top
of the tree is 35º.
1.
a. Find the height of the tree to the nearest foot.
b. Find the line of sight.

19. a. Find the height of the tree to the nearest foot.1.
Solution:
tanθ= opp/adj
tan 35°=x/47
x=47 tan35°
x=32.91 or 33 ft.

20. b. Find the line of sight.
Using Pythgorean Theroem


c=57. 43 or 57 ft

21. Try this:
A tower is 15.24 m high. At a certain distance
away from the tower, an observer determines
that the angle of elevation to the top of it is 41°.
How far is the observer from the base of the
tower?
.

22. Illustration:
Solution:
tan θ= opp/adj
tan 41°= 15.24/x
xtan 41°=15.24
x=15.24/tan 41°
x=17.53 m

23. Skills # 2
Solve for the unknown of the triangle.
An airplane is flying at a height of 4 kilometers
above the ground. The distance along the
ground from the airplane to the airport is 6
kilometers. What is the angle of depression
from the airplane to the airport?
1.

24. Illustrations:

25. Solution:
tan θ= opp/adj
tan θ=4/6
tan θ=0.6667
θ= tan-1(0.6667)
θ=33.69°

26. Try this:
Jason is on top of a 40 m cliff. He observes a boat
80m away from the base of the cliff. Find the
angle of depression from Jason to the boat.
Answer to the nearest degree?
.

27. Illustrations:
.

28. Solution:
tan θ= opp/adj
tan θ=40/80
tan θ=0.5
θ= tan-1(0.5)
θ=26.56° or 27°
.

29. GROUP ACTIVITY
The students will be divided into 5 groups and will
answer the following problems.

30. Group Activity Rules
Give thoughtful feedback
Refrain unnecessary movements and things.
On task all the time
Use soft voices
Participate actively

31. ACTIVITY: What Can I learn in the Classroom?
Instructions:
*With the same group,
Each group will select a representative to choose a
task card from their teacher.
*The class are instructed to remember the group
activity rules using the acronym GROUP.

32. Please watch the video link to know to make and use
the clinometer in mesuring angles.
https://www.youtube.com/watch?v=FVqNEBWH4B0

33. 1. What have you realized after doing the activity?
2. How did you find the height of the object?
3. What learning did you discover in doing this such
activity?

34. Generalization
1. Differentiate the angle of elevation and angle of
depression.
2. Why Angles is important in our life?

35. Evaluation
Answer the following:
Consider the situation below.
A boy who is on the second floor of their house
watches his dog lying on the ground. The angle
between his eye level and his line sight is .

36. Which angle is identified in the problem: angle of
elevation or angle of depression? Justify your
answer.
1.
2. If the boy is 3 meters above the ground,
approximately how far is the dog from the house?
3. If the dog is 7 meters from the house,
approximately how high is the boy above the ground?