geometry 8.3 trigonometry similar triangles have the same ratios of sides
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GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
SIMILAR Triangles have the same RATIOS of SIDES
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
IMPORTANT:
Sine, Cosine, and Tangent
of an Angle
Are
FRACTIONS!
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
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 SineO Opposite overH Hypotenuse
S SineO Opposite overH HypotenuseC CosineA Adjacent overH Hypotenuse
Geometry 8.3 One Way to Remember the RATIOS
S SineO Opposite overH HypotenuseC CosineA Adjacent overH Hypotenuse
T TangentO Opposite overA Adjacent
Geometry 8.3 One Way to Remember the RATIOS
SOHCAHTOA – I met him in Geometry
Sine, Cosine and Tangent – He can Calculate ALL three
(Equations)
Thank you SOHCAHTOAI’m Really Glad to Know Ya
You’re the CHIEF of Trigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
If SIMILAR Triangles have CONGRUENT Corresponding Angles
THEN
Then Angles with the SAME MeasuresMust have the SAME
SINE, COSINE and COSINE Ratios
RATIOS are Usually Shown as 4 digit DECIMALS
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
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 GEOMETRY 8.3 TrigonometryTrigonometry
45
What is :12
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
SINE Inverse (also called ARCSINE) reversesthe SIN equation:
SINOpposite
Hypotenusem A-1
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
Sine, Cosine and Tangent find SIDES
Sin-1, Cos-1 Tan-1 find ANGLE Measures
Use your Calculator to determine SIN-1 by:
• Press 2nd, then SIN• Enter the Ratio • Press ENTER to get degrees of the Angle.
SINE Inverse (also called ARCSINE) reversesthe SIN equation:
SINOpposite
Hypotenusem A-1
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
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
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 GEOMETRY 8.3 TrigonometryTrigonometry
Geometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
cIf Side a = 8 and Side c = 12
What is Angle A?
Geometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
cIf Side c = 14 and Side a = 9
What is Angle A?
Geometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 EquationsGeometry 8.3Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
cIf Side c = 22 and Side a = 6
What is Angle B?
Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
c
If Angle A = 25, and Side c = 7
What is Side a?
Geometry 8.3Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
c
If Angle A = 42, and Side a = 25
What is Side c?
Geometry 8.3Geometry 8.3 Using the SIN and SIN-1 Equations
A
B
C
a
b
c
If Angle B = 33, and Side c = 15
What is Side b?
Geometry 8.3
What is the COSINE of
30 degrees
45 degrees
60 degrees
What is the SINE of:
COSINE is Equal to
the SINE of the Angle’s Complement!
Geometry 8.3
ca
b AC
B
40
28
What is side b?
Geometry 8.3
c
a
b
A
CB
15
32What is side c?
Geometry 8.3
What is side b?
c
a
b
A
CB
15
32What is side c?
Geometry 8.3
ca
b AC
B
15
32
What is Side b?
Geometry 8.3
c
a
bA C'-
B
36
43
?
Geometry 8.3
c
a
bA C'-
B
75 ?
25
Geometry 8.3
c
a
bA C'-
B
?
7
5
Geometry 8.3
ca
b AC
B
14
15?
Geometry 8.3
c
a
b
A
CB9
13
?
Geometry 8.3
c
a
b
A
C
B
1733
?
Geometry 8.3
A BC
D
55
16
? ?
Geometry 8.3
A BC
D
10
---------------- 14 ----------------
What is Angle ADB?
Geometry 8.3
ca
b AC
Bc
m B
a
17
35
_ _ _
Geometry 8.3
ca
b AC
Bb
m A
a
16
42
_ _ _
Geometry 8.3
ca
b AC
Bb
m A
c
12
25
_ _ _
Geometry 8.3
ca
b AC
Bb
c
m B
18
33
_ _ _
Geometry 8.3
ca
b AC
Bb
a
m B
43
25
_ _ _
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 feetof HORIZONTAL distance.
What is the MAXIMUM angle that the ramp can formwith 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 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry
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