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Angles of Elevation and Depression

Angles of Elevation and Depression. Geometry. Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson. Angle of ELEVATION. l ine of sight. θ. horizontal. When you look UPWARDS…. Angle of ELEVATION. 25 feet. x. 34 0.

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Angles of Elevation and Depression

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  1. Angles of Elevation and Depression Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

  2. Angle of ELEVATION line of sight θ horizontal When you look UPWARDS…

  3. Angle of ELEVATION 25 feet x 340 Find the height of the kite if the string is 25 feet and the angle of elevation is 34 degrees.

  4. Angle of DEPRESSION horizontal θ line of sight When you look downwards…

  5. Angle of DEPRESSION 6.2 feet 460 x Find the height of the eyes of the man if he is 6.2 feet away from the basket and he makes an angle of 46 degrees.

  6. Elevation OR Depression ? B F C D A E An observer from Point ___ looks at Point ___ .

  7. The angle of elevation OR depression is the angle the line of sight makes with the horizontal. We can use trigonometric ratios to solve inaccessible distances.

  8. Take Note: Balloon Actual Distance Vertical Distance Horizontal Distance Ground Distance Football Field Ground Distance VS Vertical Distance VS Actual Distance

  9. TAKE NOTE: The actual distance is the SHORTEST distance between two objects. In a right triangle, it MAY NOT be the hypotenuse. Point B Point C Actual Distance from A to B (along vertical) Actual Distance from A to C Point A

  10. Example Which trigonometric ratio is the most appropriate to use?

  11. Example

  12. TRY THIS!

  13. TRY THIS!

  14. Word Problem • A monument is 116 meters high and casts a shadow of 196 meters. What is the angle of elevation of the sun from the ground?

  15. Word Problem • To sight the top of the building 1000 feet away, you look up 24o from the horizontal. What is the height of the building?

  16. Word Problem • If the angle of depression of the ship from the helicopter is 29o, and the helicopter is 2640 feet away (actual distance) from the ship, what is the altitude of the helicopter?

  17. Word Problem • A person in a hot air balloon that is directly over a school building sights her house. The angle of depression is 42o. The house is 1 mile from the school. Find the altitude of the balloon.

  18. Exercises

  19. Exercises SHIP 12o 40 m x wreckage

  20. Exercises

  21. Exercises About 6.8 km An airplane pilot sights a life raft. The angle of depression is 260 and the plane’s altitude is 3 km. What is the plane’s actual distance from the raft?

  22. Exercises • An observer in an airport control tower sights and airplane at an angle of elevation of 320. The pilot reports the plane’s altitude as 3.5 km. What is the airplane’s horizontal ground distance from the tower? About 5.6 km

  23. Exercises Two observers have an angle of elevation of 21 and 30 degrees to the tip of a mountain. If the two observers are 1000 meters apart, how high is the mountain?

  24. Exercises

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