ANGLES OF ELEVATION AND DEPRESSION Important concepts - The angle of elevation of a point A from a lower point O is the acute angle measured up from the horizontal line OB through point O to the line of sight, OA.

A (object)

lin

eo

ig h fs

t

Angle of elevation O

B

Horizontal line

- The angle of depression of a point P from a higher point O is the acute angle measured down from the horizontal line, OR through point O to the line of sight, OP - Teaching and Learning (Progressive Practices) - Identify the horizontal line, the angle of elevation and the angle of depression 1. For each of the following situations, identify (i) the horizontal line (ii) the angle of elevation (iii) the angle of depression Example

Q

P R

(i) Horizontal line = PR (ii) Angle of elevation = ďƒ‰ QPR (iii) Angle of depression = ďƒ‰ RPS

S

Angles of Elevation and Depression

1

-Draw a diagram to represent each of the following situations. Example

Example

Nurul is watching a plane in the sky. The plane Effendi is standing at the balcony of his house. He is 1500m above the ground. Nurul is 1.75 m observes that the angle of depression of a car, tall and the angle of elevation of the plane from which is 7 m away, is 540. 0 her eye level is 27 .

540 27

0

1500m

1.75m

7m

16.2.3 Solve each of the following problems Solving:

Example: Rashid is 1.7 m tall and Syarif is 1.05 m tall They are standing 5 m apart. Calculate the angle of depression of Syarif from Rashid. 0 0

1.7 m

RT = 1.7 – 1.05 = 0.65 m tan θ =

0.65 5

θ = tan −1

o.65 5

θ = 7.410

1.05 m 5m

Angles of Elevation and Depression

∴

The angle of depression of Syarif from Rashid is 7.41 0

2