Lesson 3- Elevation and Depression

```Done by:
Chew Tian Le (2i302)
Lee Liak Ghee (2i310)
Ng Shen Han (2i316)
Agenda
Introduction to trigonometry- Right-angled triangles, theta, etc.
Trigonometric functions
Angle of elevation
Angle of depression
Applicability in real life
Simple problems involving angles of elevation/depression
Introduction to Trigonometry


Formed from Greek words 'trigonon'
(triangle) and 'metron' (measure).
Trigonometric triangles are always rightangled triangles
More on Trigonometry
A branch of
mathematics
that studies
• Triangles
• Relationship between sides
and angles between sides
Uses
• Describes relationship
trigonometric
between sides/angles
functions
Sides of a Right-angled Triangle
Hypotenuse
• Opposite to the right-angle
• Longest side
• Side that touches θ
Opposite
• Side opposite to θ
Theta

8th letter of the Greek alphabet
Represented by “θ”
 A variable, not a constant
 Commonly used in trigonometry to
represent angle values

Trigonometric Functions



Sin (Sine)= ratio of opposite side to the
hypotenuse
Cos (Cosine)= ratio of adjacent side to the
hypotenuse
Tan (Tangent)= ratio of opposite side to the
Easier way to remember Sin, Tan, Cos
TOA CAH SOH (Big foot auntie in Hokkien)
 TOA: Tangent = Opposite ÷ Adjacent
(T=O/A)
 CAH: Cosine = Adjacent ÷ Hypotenuse
(C=A/H)
 SOH: Sine = Opposite ÷ Hypotenuse (S=O/H)

Trigonometric Functions
Angle of Elevation

The angle of elevation is the angle between
the horizontal line and the observer’s line of
sight, where the object is above the
observer
Angle of Depression

The angle of depression is the angle
between the horizontal line and the
observer’s line of sight, where the object is
below the observer
Applicability of Angles of Elevation and Depression





Used by architects to design buildings by
setting dimensions
Used by astronomers for locating apparent
positions of celestial objects
Used in computer graphics by designing 3D
effects properly
Used in nautical navigations by sailors
(sextants)
Many other uses in our daily lives
Simple Word Problem involving Angles of
Elevation


Little Tom, who is 0.75 metres tall is looking at a
bug on the top of a big wall, which is 11 times his
height. He is standing 2 metres away from the
wall. What angle is he looking up at?
Solution:
 Actual height of ceiling: 0.75m x (11)= 8.25m
 Subtract off his own body height: 8.25m - 0.75m
= 7.5m
 tan(θ) = 7.5m ÷ 2m
 tan-1(7.5 ÷ 2) = 75.1... o
Simple Word Problem involving Angles of
Depression
A boy 1m tall is standing on top of a staircase
33m high while looking at a patch of grass on the
ground 50m away from him. Find the angle from
which he is looking at.
 Solution:
• Actual height boy is looking from: 33m + 1m =
34m
• sin(θ) = 34m ÷ 50m
• sin-1(34 ÷ 50) = 42.8...o

Overall summary
•
•
•
•
Draw the diagram
Identify the known values
Form equations
Solve
We hope you have enjoyed our presentation
Thank you for your kind attention!