Transcript 5.2 Apply the Tangent Ratio

5.2 Apply the Tangent Ratio
Pg. 157
Labeling a Triangle
B
c
A
a
b
C
Vertices are labeled with Upper Case CAPITAL Letters
Sides are labeled with lower case letters, and
correspond to the angle opposite of the side
Remember the sum of all angles in a triangle is 180°
Two angles are complimentary angles if their sum is 90°
The Tangent Ratio
B
c
A
a
b
C
• Let ABC be a right triangle with acute  A .
The tangent of  A (written as tan A) is
defined as follows:
length of leg opposite A
BC
tan A 

length of leg adjacent to A AC
Real Life Problem
How tall is the tree if a 6 ft. tall
man is 60 ft. from the base and
has an angle of elevation of 37°
We will use trigonometry to solve
Trigonometry
• Trigonometry
– the study of the ___________ of _____________
• Trigonometric Ratio
– the ___________ of ___________ of ____ sides of
a _____________ triangle.
To find missing lengths of a right triangle:
Given:
1) 2 sides
To Find:
1 side
Use:
Pythagorean Theorem
2) 1 side
Other 2 sides
a) Use Special Right Triangle
IF IT IS ONE!
b) Use Trig Ratios
IF IT ISN’T “SPECIAL”!
Trigonometric ratios are great if you’re only
given 2 pieces of information
IN ADDITION TO ALREADY HAVING THE
_________ angle.
Example:
1)
2)
x
37°
18
Real Life Problem
How tall is the tree if a 6 ft. tall
man is 60 ft. from the base and
has an angle of elevation of 37°
Homework
Pg. 161, 1 – 20 all
5.3 Apply the Sine and
Cosine Ratios
Pg. 163
The Sine and Cosine Ratios
B
c
A
a
b
C
• Let ABC be a right triangle with acute  A .
The sine of  A and the cosine of  A (written
as sin A and cos A) is defined as follows:
length of leg opposite A BC
sin A 

length of hypotenuse
AB
length of leg adjacent to A AC
cos A 

length of hypotenuse
AB
3 Basic Trigonometric Ratios
• Remember, a ratio compares two things.
• We will be comparing 2 ____________
Need a reference 
Name
Abbreviation
Sine
sin
sin ( )
Cosine
cos
cos (
)
Tangent
tan
tan (
)
The reference angle is never _________
AGAIN, YOU CANNOT TAKE THE
SIN, COS, OR TAN
OF ANYTHING
UNLESS YOU HAVE
A REFERENCE ANGLE YOU’RE USING!
So how do you use these Trigonometric Ratios?
Its all about the relationships
You’ve got ________, ________, and _______
sides with trig ratios.
SOH – CAH - TOA
a=4
b=5
c=3
sin A =
sin C =
cos A =
cos C =
tan A =
tan C =
A
b=5
C
a=4
c=3
B
Why not sin B, cos B, or tan B ?
Homework
Pg. 161, 1 – 20 all