Download angle of depression

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
Adjacent
• 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
adjacent side
Easier way to remember Sin, Tan, Cos
SOH CAH TOA
 TOA: Tangent = Opposite ÷ Adjacent
(T=O/A)
 CAH: Cosine = Adjacent ÷ Hypotenuse
(C=A/H)
 SOH: Sine = Opposite ÷ Hypotenuse (S=O/H)

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
To find sides



If given two sides of the right triangle, you
can use the Pythagorean Theorem
𝑎2 + 𝑏2 = 𝑐 2
If given one side and one angle, you will use
a trigonometric function.
Finding Angles




To find angles, you have to use the inverse of
the trigonometric ratios.
Sin => sin−1
Cos => cos −1
Tan => tan−1
Example 1
• Question: You see a huge tree that is 50 feet in
height and it casts a shadow of length 60 feet.
You are standing at the tip of the shadow. What is
the degree of elevation from the end of the
shadow to the top of the tree?
Example 2

From a point 115 feet from the base of a
redwood tree, the angle of elevation to the
top of the tree is 64.3 degrees . Find the
height of the tree to the nearest foot.
Example 3

From a point 10 feet from the base of a flag
pole, the angle of elevation to the top of the
flag pole is 67.4 degrees . Find the height of
the flag pole to the nearest foot.
Example 4

If the distance from a helicopter to a tower
is 300 feet and the angle of depression is
40.2 degrees , find the distance on the
ground from a point directly below the
helicopter to the tower
Example 5

The angle of depression of one side of a
lake, measured from a balloon 2500 feet
above the lake is 43 degrees . The angle of
depression to the opposite side of the lake is
27 degrees . Find the width of the lake
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!
Please ask reasonable questions, if any.