1. Elevation and Depression زوايا الأرتفاع والانخفاض
Angles of
Elevation and Depression
زوايا الأرتفاع والانخفاض

2. eye - level

3. eye - level

4. eye - level

5. eye - level

6. eye - level

7. eye - level

8. eye - level

9. eye - level

10. eye - level

11. eye - level

12. eye - level

13. eye - level

14. eye - level
eye - level

15. eye - level
eye - level

16. The angles are equal – they are alternate angles
eye - level
eye - level
The angles are equal – they are alternate angles

17. Angle of Depression: Angle of Elevation:
Angle going DOWN from a horizontal line!
Angle of Elevation:
Angle going UP from a horizontal line!

20. A surveyor stands 200 ft from a building to measure its height with a 5-ft tall theodolite. The angle of elevation to the top of the building is 35°. How tall is the building?
Draw a diagram to represent the situation.
x = 200 • tan 35°
Solve for x.
Use the tangent ratio.
tan 35° = x
200
Use a calculator.
So x
To find the height of the building, add the height of the Theodolite, which is 5 ft tall.
The building is about 140 ft + 5 ft, or 145 ft tall.

21. 1. From a point 100 m from the foot of a building,
the angle of elevation to the top of the building is 15°.
Calculate the height of the building, correct to 1 decimal place.

22. 2. Ahmed is standing on top of a cliff, 70 m above sea level
2. Ahmed is standing on top of a cliff, 70 m above sea level. He looks directly out to sea and sights a ship at an angle of depression of 35°. Calculate the distance of the ship from shore, to the nearest metre.

23. 3. A 12 m high building casts a shadow 15 m long
3. A 12 m high building casts a shadow 15 m long. Calculate the angle of elevation of the sun, to the nearest degree.

24. 4. An airplane that is at an altitude of 1500 m is 4000 m from a ship in a horizontal direction, as shown below. Calculate the angle of depression from the airplane to the ship, to the nearest degree.