GEOMETRY 8.3 Trigonometry SIMILAR Triangles have the same RATIOS of SIDES.

GEOMETRY 8.3 GEOMETRY 8.3 TrigonometryTrigonometry


SIMILAR Triangles have the same RATIOS of SIDES


IMPORTANT:

Sine, Cosine, and Tangent

of an Angle

Are

FRACTIONS!


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


S SineO Opposite overH HypotenuseC CosineA Adjacent overH Hypotenuse

T TangentO Opposite overA Adjacent


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


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


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 !!!


45

What is :12

SINE Inverse (also called ARCSINE) reversesthe SIN equation:

SINOpposite

Hypotenusem A-1


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


Use your Calculator to determine Angle A:

If Side a = 5, and Hypotenuse c = 8



Use your Calculator to determine SIN-1 by:

• Press 2nd, then SIN• Enter the Ratio • Press ENTER to get degrees of the Angle.


Geometry 8.3Geometry 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 Trigonometry SIMILAR Triangles have the same RATIOS of SIDES.

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Transcript of GEOMETRY 8.3 Trigonometry SIMILAR Triangles have the same RATIOS of SIDES.