Download GEOMETRY 8.3 Trigonometry

GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
SIMILAR Triangles have the same RATIOS of SIDES
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
IMPORTANT:
Sine, Cosine, and
Tangent
of an Angle
Are
FRACTIONS!
GEOMETRY 8.3
Trigonometry
W A I T !!!
How can we REMEMBER to Sine, Cosine & Tangent???
SOH CAH TOA
Geometry 8.3
One Way to Remember the RATIOS
S Sine
O Opposite over
H Hypotenuse
Geometry 8.3
S
O
H
C
A
H
One Way to Remember the RATIOS
Sine
Opposite over
Hypotenuse
Cosine
Adjacent over
Hypotenuse
Geometry 8.3
S
O
H
C
A
H
One Way to Remember the RATIOS
Sine
Opposite over
Hypotenuse
Cosine
Adjacent over
Hypotenuse
T Tangent
O Opposite over
A Adjacent
SOHCAHTOA – I met him in Geometry
Sine, Cosine and Tangent –
He can Calculate ALL three
(Equations)
Thank you SOHCAHTOA
I’m Really Glad to Know Ya
You’re the CHIEF of Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
If SIMILAR Triangles have
CONGRUENT Corresponding Angles
THEN
Then Angles with the SAME Measures
Must have the SAME
SINE, COSINE and COSINE Ratios
RATIOS are Usually Shown as 4 digit DECIMALS
GEOMETRY 8.3
Trigonometry
Historically, the Ratios related with particular angles
were shown in Tables
NOW, you can find out the ratio for a particular angle
measure using your Calculator.
Make SURE your Calculator MODE is in DEGREES !!!
GEOMETRY 8.3
Trigonometry
45
1
What is :
2
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
SINE Inverse (also called ARCSINE) reverses
the SIN equation:
Opposite
SIN
 mA
Hypotenuse
-1
Sine, Cosine and Tangent find SIDES
Sin-1, Cos-1 Tan-1 find ANGLE Measures
GEOMETRY 8.3
Trigonometry
SINE Inverse (also called ARCSINE) reverses
the SIN equation:
Opposite
SIN
 mA
Hypotenuse
-1
Use your Calculator to determine SIN-1 by:
• Press 2nd, then SIN
• Enter the Ratio
• Press ENTER to get degrees of the Angle.
GEOMETRY 8.3
Trigonometry
Use your Calculator to determine SIN-1 by:
• Press 2nd, then SIN
• Enter the Ratio
• Press ENTER to get degrees of the Angle.
Use your Calculator to determine Angle A:
If Side a = 5, and Hypotenuse c = 8
If Side a = 10, and Hypotenuse c = 40
If Side a = 15, and Hypotenuse c = 18
Geometry 8.3
Using the SIN and SIN-1 Equations
C
a
b
B
c
If Side a = 8 and
Side c = 12
A
What is Angle A?
Geometry 8.3
Using the SIN and SIN-1 Equations
C
a
b
B
c
If Side c = 14 and
Side a = 9
A
What is Angle A?
Geometry 8.3
Using the SIN and SIN-1 Equations
C
a
b
B
c
If Side c = 22 and
Side a = 6
A
What is Angle B?
Using the SIN and SIN-1 Equations
Geometry 8.3
B
If Angle A = 25, and
Side c = 7
c
What is Side a?
a
C
b
A
Using the SIN and SIN-1 Equations
Geometry 8.3
B
If Angle A = 42, and
Side a = 25
c
What is Side c?
a
C
b
A
Using the SIN and SIN-1 Equations
Geometry 8.3
B
If Angle B = 33, and
Side c = 15
c
What is Side b?
a
C
b
A
Geometry 8.3
COSINE is Equal to
the SINE of the Angle’s Complement!
What is the COSINE of
30 degrees
45 degrees
60 degrees
What is the SINE of:
Geometry 8.3
B
What is side b?
c
a
28
40
C
b
A
Geometry 8.3
15
a
C
32
b
A
B
c
What is side c?
Geometry 8.3
15
a
C
B
What is side c?
32
What is side b?
b
A
c
Geometry 8.3
What is Side b?
B
15
c
a
32
C
b
A
Geometry 8.3
B
36
c
a
43
A
?
b
- C'
Geometry 8.3
B
75
?
c
a
A
25 b
- C'
Geometry 8.3
B
?
5
c
a
A
7
b
- C'
Geometry 8.3
B
?
a
C
15
14 b
c
A
Geometry 8.3
a 9 B
C
?
b
c
13
A
Geometry 8.3
b
C
A
a 17
33
c
?
B
Geometry 8.3
D
16
55
A
?
C
?
B
Geometry 8.3
D
What is Angle ADB?
10
A
C
----------------
14
B
----------------
Geometry 8.3
c  17
B
c
a
C
b
m B  35
a  ___
A
Geometry 8.3
b  16
B
c
a
C
b
m A  42
a  ___
A
Geometry 8.3
b  12
B
c
a
C
b
m A  25
c  ___
A
Geometry 8.3
b  18
B
c
a
C
b
c  33
m B  _ _ _
A
Geometry 8.3
b  43
B
c
a  25
m B  _ _ _
a
C
b
A
Geometry 8.3
A water slide is a straight ramp 25 meters long
that starts from the TOP of a tower 21 meters tall.
Find the ANGLE the slide forms with the Tower.
Geometry 8.3
According to the Americans with Disabilities Act,
a ramp can RISE no more than 1 foot for every 12 feet
of HORIZONTAL distance.
What is the MAXIMUM angle that the ramp can form
with the ground?
Geometry 8.3
The Grade of the Pike’s Peak cog railway is 18 percent.
That is, for every 100 feet of horizontal run, the train
RISES 18 feet.
Find the angle of the inclination of the railway.
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry
GEOMETRY 8.3
Trigonometry