Download Right Triangle Trigonometry

Right Triangle Trigonometry
May 16, 2014
What's Going On?
Reference Angles
The Trigonometric Ratios
Setting up to solve.
Learning Goal ­ I will understand when to use each trigonometric ratio to solve a right­triangle problem.
Right Triangle Trigonometry
May 16, 2014
New Unit
Trigonometry
Right Triangle Trigonometry
May 16, 2014
Labelling a Triangle
When we deal with triangles, we need to be
able to properly label all of the sides and all
of the __________.
Angles are labelled with ______________
letters, __________ are labelled with
lower case letters. We always label sides
based on their ________________ angles.
B
A
C
Right Triangle Trigonometry
May 16, 2014
Reference Angles
When we are exploring ________________
triangles, we typically have what is called a
_____________________________ angle .
We use a ______________________ angle
so that we can easily talk about different
sides of the triangle without it being
confusing.
A
B
C
Right Triangle Trigonometry
May 16, 2014
Reference Angles
Once we have chosen our ______________
angle we can refer to the three sides of a
right triangle as the:
opposite side
adjacent side
hypotenuse
Right Triangle Trigonometry
May 16, 2014
The Angle Monster
B
hypotenuse
opposite side
A
C
adjacent side
The angle monster always looks at his opposite side and
hugs his adjacent side and his hypotenuse.
Right Triangle Trigonometry
May 16, 2014
The Angle Monster
B
hypotenuse
adjacent side
A
opposite side
C
The angle monster always looks at his opposite side and
hugs his adjacent side and his hypotenuse.
Right Triangle Trigonometry
May 16, 2014
Reference Angles
G
opposite: ___
adjacent: ___
hypotenuse: ___
H
Without a reference angle, we can't do this!!
I
Right Triangle Trigonometry
May 16, 2014
Reference Angles
G
Reference Angle: ___
opposite: ___
adjacent: ___
hypotenuse: ___
H
Without a reference angle, we can't do this!!
I
Right Triangle Trigonometry
May 16, 2014
Reference Angles
Reference Angle: ___
opposite: ___
M
adjacent: ___
hypotenuse: ___
N
O
Right Triangle Trigonometry
May 16, 2014
Reference Angles
Reference Angle: Z
opposite: ___
adjacent: ___
X
hypotenuse: ___
Y
Z
NEVER USE THE RIGHT
o
ANGLE (90 ) AS A
REFERENCE ANGLE!!!!
Right Triangle Trigonometry
May 16, 2014
Fillin' in the Blanks
Use your notes to fill in the blanks.
Stop when you get to "The Ratios"
Right Triangle Trigonometry
May 16, 2014
5 m
3 m
4 m
Ratios of Sides
Right Triangle Trigonometry
May 16, 2014
5 m
3 m
4 m
8 m
Right Triangle Trigonometry
May 16, 2014
10 m
6 m
5 m
3 m
4 m
8 m
Ratios of Sides
Right Triangle Trigonometry
May 16, 2014
10 m
6 m
5 m
3 m
4 m
8 m
12 m
Right Triangle Trigonometry
May 16, 2014
15 m
10 m
9 m
6 m
5 m
3 m
4 m
8 m
12 m
Ratios of Sides
Right Triangle Trigonometry
May 16, 2014
For any given reference angle, the ratios of the sides (opposite, adjacent, hypotenuse) are the same!!!
always ___________________!
15 m
10 m
9 m
6 m
5 m
3 m
4 m
8 m
12 m
Ratios of Sides
Right Triangle Trigonometry
May 16, 2014
These ratios are so special that they have been given special names!
Do you remember what they are???
Ratios of Sides
Right Triangle Trigonometry
May 16, 2014
The Trigonometric Ratios
opposite
sin (angle) = _____________
hypotenuse
The "sine" of an angle tells you the ratio of opposite
the side ____________________ the angle hypotenuse
to the ______________________.
adjacent
cos (angle) = _____________
hypotenuse
The "cosine" of an angle tells you the ratio adjacent
of the side ____________________ the hypotenuse
angle to the ______________________.
opposite
tan (angle) = _____________
adjacent
The "tangent" of an angle tells you the ratio opposite
of the side ____________________ the angle adjacent
to the side ___________________ the angle.
Right Triangle Trigonometry
May 16, 2014
Fillin' in the Blanks II
Use your notes to fill in the rest of the blanks on your sheet.
Put the sheet into your unit book!
Right Triangle Trigonometry
May 16, 2014
The Ratios
B
c
A
sin A = sin B = b
cos A = cos B = a
C
tan A = tan B = Right Triangle Trigonometry
May 16, 2014
The Ratios
B
c
A
2 m
23o
b
Solve for side b
Solve for side c
C
Right Triangle Trigonometry
May 16, 2014
The Ratios
B
11 m
4 m
A
b
Solve for angle A
Solve for angle B
C
Right Triangle Trigonometry
May 16, 2014
Practicing the Skills
Use your iPad notes and your handout to work through the examples on your sheet.
You don't need to actually solve yet, just set it up to solve it!
Right Triangle Trigonometry
May 16, 2014
The Primary Trigonometric Ratios
sin (angle) = opposite
hypotenuse
soh
cos (angle) = adjacent
hypotenuse
cah
tan (angle) = opposite
adjacent
toa
Right Triangle Trigonometry
It's amazing!
May 16, 2014
YES!!!!
sohcahtoa
U
YO E
V
LO !
IT