1. Angles of Elevation
and Depression

2. Angle of Elevation

3. When you see an object above you

4. When you see an object above you
Angle of Elevation
line of sight
horizontal
You
There is an angle of elevation between the horizontal and your line of sight to the object

5. When you see an object above you
Angle of Elevation
line of sight
horizontal
You
You can use Trigonometry to find distances from the Angle of Elevation Information

6. Example

7. Angle of Elevation 20º Door ramp 4 ft horizontal ground level
A homeowner is to construct a ramp to his front door to make it wheelchair-accessible. How long is the ramp if the door is 4 ft above ground level and the angle of elevation is 200
Door
ramp
Angle of Elevation
4 ft
20º
Bottom of Ramp
horizontal ground level

8. Let x = the length of the ramp
A homeowner is to construct a ramp to his front door to make it wheelchair-accessible. How long is the ramp if the door is 4 ft above ground level and the angle of elevation is 200 x
4 ft
20º
Let x = the length of the ramp

9. The length of the ramp should be 11.7 ft
A homeowner is to construct a ramp to his front door to make it wheelchair-accessible. How long is the ramp if the door is 4 ft above ground level and the angle of elevation is 200
The length of the ramp should be 11.7 ft x
4 ft
20º

10. Another
Example

11. One is at a 62º angle of elevation
A bystander notices two window washers on the side of a building, one straight up from the other.
One is at a 62º angle of elevation
And the other at a 30º angle of elevation.
If the bystander is 42 ft from the point at the base of the wall directly below the window washers,
How far apart are the window washers?

12. From 42 ft from the base of the wall
62º 42
62º
angle of elevation
From 42 ft from the base of the wall
A bystander notices two window washers on the side of a building, one straight up from the other One is at a 62º angle of elevation and the other at a 30º angle of elevation If the bystander is 42 ft from the point at the base of the wall directly below the window washers, How far apart are the window washers?

13. From 42 ft from the base of the wall
30º 42
30º
angle of elevation
From 42 ft from the base of the wall
A bystander notices two window washers on the side of a building, one straight up from the other One is at a 62º angle of elevation and the other at a 30º angle of elevation If the bystander is 42 ft from the point at the base of the wall directly below the window washers, How far apart are the window washers?

14. x y
62º
30º 42
Let x = distance from the ground of the highest window washer
Let y = distance from the ground of the lowest window washer
Then x – y = distance between the window washers

15. x
62º 42
Let x = distance from the ground of the highest window washer

16. x
62º 42
Let x =

17. x y
62º
30º 42
Let x =
Let y = distance from the ground of the lowest window washer

18. y
30º 42
Let y = distance from the ground of the lowest window washer

19. x y
62º
30º 42
Let x =
Let y =

20. x y
62º
30º 42
Let x =
Let y =
Then x – y = distance between the window washers

21. The Window Washers are 54.7 ft apartx y
62º
30º 42
The Window Washers are 54.7 ft apart

22. You Try

23. The world’s tallest fountain is in Fountain Hill, Arizona
The world’s tallest fountain is in Fountain Hill, Arizona If the angle of elevation to the top of the fountain from a point 755 ft from its base is , find the height of the fountain
Solution Next Slide

24. The height of the fountain is 558.7 ft
The world’s tallest fountain is in Fountain Hill, Arizona If the angle of elevation to the top of the fountain from a point 755 ft from its base is , find the height of the fountain x
36.5º
755
The height of the fountain is ft

25. Angle of Depression

26. When you see an object below you

27. When you see an object below you
horizontal
Angle of Depression
line of sight
Object
There is an angle of depression between the horizontal and your line of sight to the object

28. We make use of the angle of elevation between the the two objects
When given an angle of depression between the horizontal and your line of sight to the object.
We make use of the angle of elevation between the the two objects
To Solve Problems

29. Angle of Elevation Angle of Depression You horizontal line of sight
Object
The angle of depression between the horizontal and your line of sight to the object is equal to the angle of elevation between the the two objects

30. The angle of depression and the angle of elevation are alternate interior angles and therefore equal

31. Angle of Elevation Angle of Depression You horizontal line of sight
Object
The angle of depression between the horizontal and your line of sight to the object is equal to the angle of elevation between the the two objects

32. Example

33. A building casts a shadow 42 m long
A building casts a shadow 42 m long The angle of depression from the top of the building to the tip of the shadow is 53° Determine the height of the building. Draw a diagram.
Shadow
42 m

34. A building casts a shadow 42 m long
A building casts a shadow 42 m long The angle of depression from the top of the building to the tip of the shadow is 53° Determine the height of the building. Draw a diagram.
53º
42 m

35. Let x = the height of the building
A building casts a shadow 42 m long The angle of depression from the top of the building to the tip of the shadow is 53° Determine the height of the building. Draw a diagram.
53º x
53º
42 m
Let x = the height of the building

36. The height of the building is 55.7 m
A building casts a shadow 42 m long The angle of depression from the top of the building to the tip of the shadow is 53° Determine the height of the building. Draw a diagram. x
53º
42 m
The height of the building is 55.7 m

37. Another
Example

38. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.

39. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
150

40. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
220
150

41. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
220
Angle of Depression
150

42. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
220
Angle of Depression
370
150

43. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
Angle of Depression
370

44. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
14º
Angle of Depression
370

45. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
14º
370
14º

46. 14º 370 x Let x = the distance from the ship to the base of the cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
370
14º x
Let x = the distance from the ship to the base of the cliff

47. A lighthouse 220 ft tall sits on the edge of a 150 ft cliff
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
370
14º x

48. The distance from the ship to the base of the cliff is 1,484 ft
A lighthouse 220 ft tall sits on the edge of a 150 ft cliff The angle of depression from the top of the lighthouse to a ship at sea is 14° Determine the distance from the ship to the base of the cliff. Draw a diagram.
370
14º x
The distance from the ship to the base of the cliff is 1,484 ft

49. You Try

50. The angle of depression of an airplane to the airport is 30
The angle of depression of an airplane to the airport is 30.1 when the plane is km from the airport measured along the ground Determine the altimeter reading inside the plane or in other words the height of the plane from the ground.
(Make a sketch, label all given angles and dimensions – Round to the nearest tenth)
Solution Next Slide

51. The Altimeter reading is 5.97 km
The angle of depression of an airplane to the airport is 30.1 when the plane is km from the airport measured along the ground Determine the altimeter reading inside the plane or in other words the height of the plane from the ground.
(Make a sketch, label all given angles and dimensions – Round to the nearest hundredth)
30.1º x
30.1º
10.3 km
The Altimeter reading is 5.97 km