Section 4.3
Right Triangle Trigonometry
Right Triangle Definitions of Trigonometric Functions
Mnemonic device: SOH-CAH-TOA
Trigonometry values for a given angle are
always the same no matter how large the
triangle is
Example
Find the value of each of the six trigonometric functions
of  if b=4 and c=2 5.
c2 5
b4
Function Values for Some Special Angles
Example
Find the csc 300 , sec 300 , cot 300
Example
Find the csc 600 , sec 600 , cot 600
Trigonometric Functions and Complements
Example
Find a cofunction with the same value as the given expression:
cos 20o
cot 40o
Applications
An angle formed by a horizontal line and the line
of sight to an object that is above the horizontal
line is called the angle of elevation. The angle formed
by a horizontal line and the line of sight to an object
that is below the horizontal line is called the angle of
depression. Transits and sextants are instruments
used to measure such angles.
Example
The irregular blue shape is a pond. The distance across
the pond, a, is unknown. To find this distance, a
surveyor took the measurements shown in the figure.
What is the distance across the pond?
1200 yards
The inverse function for tangent and the other angles
can be accessed on your calculator the same way.
Example
A building is 40 feet high and it casts a shadow
36 feet long. Find the angle of elevation of the
sun to the nearest degree.
40 feet
36 feet
Find the cos  .
1
3
3 10
10
(b) 3
10
(a)
10
10
1
(d)
10
(c)
Find the height of the tree if the length of the
shadow is 50 feet when the sun is at a 300 angle.
(a) 25 feet
(b) 25.56 feet
(c) 28.87 feet
(d) 30 feet
30o
50 feet