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ANGLE AND PLANE

ANGLE AND PLANE. Identify Angle. ANGLE AND PLANE. Determining position of line, and angle that involves point, line and plane in two-dimension. Standard Competence:. Base Competence:.

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ANGLE AND PLANE

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  1. ANGLE AND PLANE Identify Angle

  2. ANGLE AND PLANE Determining position of line, and angle that involves point, line and plane in two-dimension. Standard Competence: Base Competence: • Identifying angle.2. Identifying the circumference of flat shape and width of flat shape.3. Applying transformation of flat shape. ANGLE AND PLANE

  3. B’ B’ B B Dinamai sudut BAB’ atau BAB’ atau A atau α Mentioned as angle BAB’ orBAB’ or A orα 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 : α ANGLE AND PLANE

  4. Y C θ θ A X Angleθis not in base position Angleθis in base position Kinds of Angle Unit Angle in Base Position Side AB is called beginning side from angleθ Side AC is called limit side from angleθ ANGLE AND PLANE

  5. Seksagesimal Angle Size Radial Sentisimal Kinds of angle unit Angle Size ANGLE AND PLANE

  6. 1 radian r Kinds of angle unit Radial System 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 ANGLE AND PLANE

  7. 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”) ANGLE AND PLANE

  8. 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 ANGLE AND PLANE

  9. Width and Circumference of flat shape A. The width place arranged plane 1. Triangle Width: A L = ½ A x t Where, A = base wide, t = tall C B Example: A Calculate the width and circumference plane beside. 12 13 C B Answer:AB = = = = = 24 ANGLE AND PLANE

  10. A b c t C B a The width and circumference of flat plane Next! Triangle width: Triangle circumference:K = AB + BC+ AC = 13 cm + 12 cm +5 L = == 84 = 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: Or L = With s = Circumference (K)= a + b + c Triangle width (L) = ANGLE AND PLANE

  11. Width and the circumference of flat plane 2. Square Width • 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 ANGLE AND PLANE

  12. Width and circumference of flat plane 3.Width and circumference of circle Width Formula in every circle is: Width = πx radius x radius = π x r x r = πr2 Circle circumference = 2 r by π = 3,14 or π = ANGLE AND PLANE

  13. 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 ANGLE AND PLANE

  14. Width and circumference of flat shape 5. Width and circumference of parallelogram Example: Parallelogram has sides a and b and tall t b t a 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 cm2Circumference = 2 ( 7 cm + 5 cm) = 2 x 12 cm = 24 cm ANGLE AND PLANE

  15. Width and circumference of flat shape 6. Width and circumference of kites Kite ABCD D A C B Width (L)= ½ (a xb) a b 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 ANGLE AND PLANE

  16. Find the trapezium width in the picture! D E C 8 10A B 15 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 Example: Answer: Width = ½ ( AB + CD) CE = = = = ANGLE AND PLANE

  17. Side n arranged which has length = aL = a2 x ctg ½ a a Sample:Width of 6 side arrangedL = Width and circumference of flat plane 8. Area width side n arranged ANGLE AND PLANE

  18. Width and circumference of flat plane 9. Area width of ellipse b Area width of ellipse if the axis mayor = a and axis minor = b then:L = ab a ANGLE AND PLANE

  19. M I E K G C o1 o2 o3 o4 o5 o6 O 7 A See! L N B D F H J d Area width in irregular plane 1. Trapesoida Rule • Part width ABCD = ½ (O1 + O2), and so are the other parts, then gotten part or total width as total of all parts width. Width = part width. Width= d . ANGLE AND PLANE

  20. E C d A yy y2 y3 B D F 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 Total part width = y1 . d + y2 . d+ y3 . d+ …. ANGLE AND PLANE

  21. M I E K G 2 C A 5 7 10 8 12 913 L N B D F H J 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 ANGLE AND PLANE

  22. Area width of irregular plane area Nextb. Mid Ordinate y1 = , y2 = , y3= , y4= y5= , y6 = 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 ANGLE AND PLANE

  23. Thank you Keep practicing!… The end ANGLE AND PLANE

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