ANGLE AND PLANEANGLE AND PLANE

Identify Angle

Hal.: 2 ANGLE AND PLANE Adaptif

Determining position of line, and angle that involves point, line and plane in two-dimension.

1. Identifying angle.

2. Identifying the circumference of flat shape and width of flat shape.

3. Applying transformation of flat shape.

ANGLE AND PLANE

Standard Competence:

Base Competence:

Hal.: 3 ANGLE AND PLANE Adaptif

Kinds of Angle Unit

Definition of Angle

In taxonomy study, according to Gagne, angle is a base concept, so from several ways to define about angle, is that by one approach through line rotation as follows :

Dinamai sudut BAB’

atau BAB’ atau A atau α

B’

BMentioned as angle BAB’

or BAB’ or A or α

B’

Bα

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Angle in Base Position

Kinds of Angle Unit

θ

Angle θ is not in base position

X

Y

A

C

θ

Angle θ is in base position

Side AB is called beginning side from angle θ

Side AC is called limit side from angle θ

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Angle Size

Kinds of angle unit

Angle Size

Seksagesimal

Radial

Sentisimal

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Radial System

Kinds of angle unit

r1 radian

As motivation, it is told that in measuring elevation angle, Merriam shoot in military was needed angle size and didn’t use degree measurement, unless the other normal measurement we know as radiant system

In radiant system the center angle size is of a circle that the length of busur in front of the angle is equal to radius of that circle.

Then gotten a relation:

1800 = π radian

1 radian

radian

"45'175757,296 00

017453,010

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Kinds of Angle Unit

Centesimal System The instruments for astronomy, peneropongan

bintang, teodolit known as different angle unit with both measurement above, this system is known centesimal system. A full rotation is 400g

in this system (read “400 grad”). So the angle size ½ rotation is 200g Angle size ¼ rotation is 100g Angle

size 1/400 rotation is 1g For the smaller angle size known as : 1g = 10dgr = 10 ( read : “10 decigrad”

) 1dgr = 10cgr = 10 (read : “10

centigrad”) 1cgr = 10 mgr = 10 (read : “10 miligrad”) 1mgr = 10 dmgr =

10(read :“10decimiligrad”)

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Angle Conversion

Conversion of angle size Degree Unit = radian unit = grad

3600 = 2 radian = 400g

1 radian = 57,3250 = 63,694g

10 = 0,0174 radian = 1,11g

1g = 0,90 = 0,0157 radian 1° = 60’ = 3600” second

Example:Change 300 into radian unit and grade!

Answer:300 = 30 x 0,0174 radian = 0,522 radian300 = 30 x 1,11 g = 33,3 g

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Width and Circumference of flat shape

22 ACBC 22 725

1. Triangle Width:

L = ½ A x t

Example:

Where, A = base wide, t = tall

A

C B

A

C B 13

12

Calculate the width and circumference plane beside.

Answer: AB = = = = = 24

49625 576

A. The width place arranged plane

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The width and circumference of flat plane

2

ta

2

ACAB2

724

Triangle width:

L =

= = = 84

Triangle circumference:K = AB + BC+ AC = 13 cm + 12 cm +5

So, the triangle width is 84 cm2 and the circumference is 56 cm

1.1 If the triangle has side a, b, c and triangle high that base right

stand is t, then:

Triangle width (L) =2

ta

Or L = ))()(( csbsass

With s = C t

a B

Ab

c

Circumference (K)= a + b + c

2

cba

Next!

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Width and the circumference of flat plane

The formula of width in every square is:

Width = side length X side length

L = s x s

L = s2

Circumference (K) = 4 x side

2. Square Width

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Width and circumference of flat plane

Width Formula in every circle is:

Width = π x radius x radius

= π x r x r

= πr2

Circle circumference = 2 r

by

π = 3,14or

π =

3. Width and circumference of circle

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Width and Circumference of flat plane

4. Width and circumference of rectangular

Rectangular ABCDA p B

C D

Width ABCD = p x

Circumference ABCD = (2 x p) + ( 2 x )

Example:Rectangular ABCD, the length is 8 cm and wide is 6 cm. Determine the width and circumference of that rectangular!

Answer:Rectangular width = p x = 8 x 6 = 48 Rectangular circumference = (2 x p) + (2 x ) = (2 x 8) + ( 2 x 6) = 16 + 12 = 28

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Width and circumference of flat shape

5. Width and circumference of parallelogram

b t a

Example: Parallelogram has sides a and b and tall t

Parallelogram width (L)= a x t

Parallelogram circumference (K)= 2 (a + b)

Example:Find the width and the circumference of Parallelogram in the picture below!

Answer: 7 5 4

Width = 7 cm x 4 cm = 28 cm2

Circumference = 2 ( 7 cm + 5 cm) = 2 x 12 cm = 24 cm

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Width and circumference of flat shape

6. Width and circumference of kites

Kite ABCD D A C

B

Width (L)= ½ (a xb)

ba Circumference= AB+BC+CD+DA

Example:

Find the width of kite below, if the diagonal line is AC = 10 cm and BD= 8 cm.

D Answer:

Width = ½ ( AC x BD)

A C = ½ ( 10 cm x 8 cm ) = 40 cm2

B

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Width and circumference of flat plane

7. Width and circumference of Trapezium A B Width = ½ ( AB + CD) . t t Circumference = AB + BC + CD +

DA

C D

22 BEBC

Example:Find the trapezium width in the picture! D E C 8 10

A B 15

Answer: Width = ½ ( AB + CD) CE = =

22 810 = = 64

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Width and circumference of flat plane

8. Area width side n arranged

Side n arranged which has length = a

L = a2 x ctg n

01804

n

Sample:Width of 6 side arranged

L = 34

6 2a

½ aa

3

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Width and circumference of flat plane

9. Area width of ellipse

Area width of ellipse if the axis mayor = a and axis minor = b then:L = ab

a

b

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Area width in irregular plane

1. Trapesoida Rule

Width = part width.

Width= d .

65432

71 (2

ooooooo

ateotherordin

telastordinaatefirstordin

2

•Part width ABCD = ½ (O1 + O2), and so are the other parts, then gotten part or total width as total of all parts width.

See!

A

M

K

I

G

E

C

DB F H J NL

d

o1 o2 o3 o4 o5 o6 O 7

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Area width of irregular plane

2. Mid Ordinate Rule

y1, y2, … shows ordinate in the middle last ordinate.

y1 = , y2 =

Part width ABCD= y1 x d and width CDEF = y2 x d

2

CDAB

2

EFCD

Total part width = y1 . d + y2 . d+ y3 . d+ ….

F

E

D

C

B

A

yy y2 y3

d

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Area width of irregular plane

Example of irregular plane

Determine irregular plane width beside by rules:a. Trapesoidab. Mid Ordinate

Answer:a. Trapesoida Rule

L = 2.

L =2 . L = 2 . 47 = 94

65432

71

2OOOOO

OO

9121087

2

135

5 7 10 8 12 9 13 A

M

K

I

G

E

C

DB F H J NL

2

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Area width of irregular plane area

Next

b. Mid Ordinate

y1 = , y2 = , y3= , y4=

y5= , y6 =

62

75

5,8

2

107

8

2

810

10

2

128

5,102

912

6

2

39

Total width = y1 .d + y2. d+ y3. d + y4. d+ y5. d+ y6. d = 6 . 2 + 8,5. 2 + 8 . 2 + 10 . 2+ 10,5 . 2 + 6 . 2 = 12 + 17 + 16 + 20 + 21 + 12 = 98

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Thank you

Keep practicing!…

The end