Chapter 11Angles of Elevation and Depression

Prepare by Miss Chai Choy FahSMK Lake, Bau

Angle of elevation

• Angle between horizontal line through point of observation and the line of sight of an object that lies above horizontal line.

Look at the bird, my eye is moving upward, so,

line of sight is

horizontal line.

Angle of elevation

is at below line of sight

above

Angle of depression• Angle between horizontal line

through point of observation and the line of sight of an object that lies below horizontal line.

I’m looking at the boy, my eye is moving downward, so, line of sight is

horizontal line.

Angle of depression

is at above line of sight.

below

EXAMPLES:

State the angle of elevation from point Q to point P.

Determine the line of sight.

The is below the line of sight.

• Q

• P

• R

• S

Determine the horizontal line.

Determine the angle of elevation.

Angle of elevation:

RQP

State the angle of depression from point P to point Q.

Determine the line of sight.

• Q

• P

• R

• S

Determine the horizontal line.

Determine the angle of depression.

Angle of depression:

SPQ

The is above the line of sight.

EXERCISE:

Steven was looking at a bird from far. Based on the diagram, find the angle of depression from the bird to Steven.

1.5 m

A

B

C D

E

1177.93 m

500 m

Highlight the important information given first.

F

Question 1:

1.5 m

A

B

C D

E

1177.93 m

500 m

Step 1: Draw the line of sight.

Step 2: Draw the horizontal line. The horizontal line is above the line of sight.

Step 3: Get the triangle. The is above the line of sight.

Step 4: Get the angle of depression.

Angle of depression:

FAE

F

Calculation:

By using trigonometry:

m

mFAE

500

93.1177tan

35586.2tan FAE

35586.2tan 1FAEoFAE 67

Angle of depression: oFAE 67

Question 2:Based on the diagram given, calculate the height of the flagpole.

3.0 m

10 m

37o

The boy is looking to the flagpole, so his head is moving upward.

The angle that related will be

angle of elevation.

3.0 m

10 m

37o

Step 1: Determine the line of sight.

Step 2: Determine the horizontal line. The horizontal line is below the line of sight.

Step 3: Complete the triangle.

y

10 m

Step 4: Determine the angle of elevation.

Step 5: Label the missing information.

Angle of elevation = 37o

Height of flagpole

Calculation:

By using trigonometry:

m

yo

1037tan

1075.0

y

1075.0y

my 5.7

Height of the flagpole: 7.5m + 3m = 10.5 m