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Three Dimensional Geometry ( Geometri Dimensi Tiga )

Three Dimensional Geometry ( Geometri Dimensi Tiga ). Angle in three dimensional ( sudut dalam dimensi tiga ). Learning Objectives ( Tujuan Pembelajaran ). Determining angles between two lines ( menentukan sudut antara garis dan bidang ) Determining angles between line and plane

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Three Dimensional Geometry ( Geometri Dimensi Tiga )

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  1. Three Dimensional Geometry(GeometriDimensiTiga) Angle in three dimensional (sudutdalamdimensitiga)

  2. Learning Objectives(TujuanPembelajaran) • Determining angles between two lines (menentukansudutantaragarisdanbidang) • Determining angles between line and plane (menentukansudutantaragarisdanbidang) • Determining angles between two planes (menentukansudutantaraduabidang)

  3. Perhatikanbahwa: Sudut-sudutdalamruangdapatdibentukolehduaunsur: • Garisdangaris • Garisdanbidang • Bidangdanbidang

  4. Measure of angles in three dimension • Angles between line and line • Angle between line and plane • Angle between two plane

  5. Angle between line and line • Sudut antara

  6. Angle between line and line b besarsudutantaraduagarisadalahbesarsudutterkecil yang dibentukolehkedua garistersebut a

  7. H G E F D C A B Contoh: Diketahui kubus ABCD.EFGH Besar sudut antara garis-garis: a. AB dengan AH b. BG dengan BE c. AF dengan CH

  8. Pembahasan Besarsudutantara garis-garis: a. AB dengan AH = 90º b. BG dengan BE = 60º Karenasegitiga BEG adalahsegitigasamasisidimanasisi-sisinyamerupakan diagonal bidangkubus, sehingga BG=BE=EG c. AF dengan CH = 90º Karena AF tegaklurus CH (duagarisbersilangan) H G E F D C A B

  9. Angle between line and plane Sudutantaragarisa danbidangdilambangkan(a,)adalahsudutantara garis a dan proyeksinyapada . Perhatikangambardisamping! SudutantaragarisMN denganbidang V = sudutantaraMN dengan M’N =  MNM’ M N V M’

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