Presentasi matematika-kelas-x-dimensi-tiga

Dimensi Tiga ( Proyeksi & Sudut ) http://meetabied.wordpress.com

Setelah menyaksikan tayangan ini anda dapat Menentukan proyeksi dan besar sudut dalam ruang dimensi tiga http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],P Q k m http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],T http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],B T A’ A’ (AC  ET) (AB  BC) (AC  BD) http://meetabied.wordpress.com A B C D H E F G T

[object Object],Dari titik P di luar bidang H ditarik garis g  H. Garis g menembus bidang H di titik P’. Titik P’ adalah proyeksi titik P di bidang H P P’ g http://meetabied.wordpress.com H

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(EA  ABCD) A P P http://meetabied.wordpress.com A B C D H E F G

[object Object],Proyeksi sebuah garis ke sebuah bidang dapat diperoleh dengan memproyek- sikan titik-titik yang terletak pada garis itu ke bidang. A A’ g Jadi proyeksi garis g pada bidang H adalah g’ B B’ g’ http://meetabied.wordpress.com H

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],b. Jika panjang rusuk kubus 6 cm, Panjang proyeksi garis CG pada bidang BDG adalah…. http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Jadi proyeksi EF pada ABCD adalah garis AB http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Jadi proyeksi CG pada BDG adalah garis PG dan panjangnya? P 6 cm http://meetabied.wordpress.com A B C D H E F G

• Panjang proyeksi CG pada BDG adalah panjang garis PG . • PG = ⅔.GR = ⅔.½a√6 = ⅓a√6 = ⅓.6√6 P R • Jadi panjang proyeksi garis CG pada bidang BDG adalah 2√6 cm 6 cm http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],16 cm 18 cm http://meetabied.wordpress.com T A D C B

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],16 cm 18 cm T’ Jadi panjang proyeksi TA pada bidang ABCD adalah 8 √2 cm http://meetabied.wordpress.com T A D C B

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],k m http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],P’ http://meetabied.wordpress.com P Q V

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],6 cm Kemudian hitunglah besar sudutnya! http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],6 cm Jadi  (BG,ACGE) =  (BG,KG) =  BGK K http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],6 cm sin  BGK = Jadi, besar  BGK = 30 0 K http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],8 cm Nilai tangens sudut antara garis CG dan bidang AFH adalah…. http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8 cm P Q Nilai tangens sudut antara garis CG dan bidang AFH adalah ½√2 http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],sudut antara TA dan bidang ABCD adalah…. http://meetabied.wordpress.com T A B C D a cm a cm

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],sudut antara TA dan bidang ABCD adalah sudut antara TA dan AC yang besarnya 45 0 http://meetabied.wordpress.com T A B C D a cm a cm

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],  (  ,  ) g h http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Jadi  (BDG,ABCD) =  (GP,PC) =  GPC P http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Jadi, sin  (BDG,ABCD) = ⅓√6 P http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://meetabied.wordpress.com A B C T 6 cm 9 cm

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],P 3 http://meetabied.wordpress.com A B C T 6 cm 9 cm

• Lihat ∆ TPC PT = 6√2, PC = 3√3 Aturan cosinus TC 2 = TP 2 + PC 2 – 2TP.TC.cos  TPC 81 = 72 + 27 – 2.6√2.3√3.cos  TPC 36√6.cos  TPC = 99 – 81 36√6.cos  TPC = 18 cos  TPC = = A B C T 9 cm P 6 √2 3 √3 2 1 http://meetabied.wordpress.com

• Lihat ∆ TPC cos  P = Maka diperoleh Sin  P = Jadi sinus  (TAB,ABC) = 12 √ 6 P http://meetabied.wordpress.com

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Sudut antara bidang FHQP dan bidang AFH adalah  . Nilai cos  =… 4 cm P Q http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],4 cm P Q K L  M http://meetabied.wordpress.com A B C D H E F G

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],K L  M A Jadi nilai cos  = http://meetabied.wordpress.com

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