mathematics module
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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
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