Iklan

Iklan

Pertanyaan

Diketahui kubus ABCD.EFGH. titik M berada di rusuk AD sedemikian sehingga AM : MD = 1 : 2. Titik N berada di rusuk CD sedemikian sehingga CN : ND = 1 : 2. Titik P berada di rusuk DH sedemikian sehingga DP : PH = 2 : 1. Jika α adalah sudut antara bidang MNP dan garis PB maka nilai cos ⁡α = ….

Diketahui kubus ABCD.EFGH. titik M berada di rusuk AD sedemikian sehingga AM : MD = 1 : 2. Titik N berada di rusuk CD sedemikian sehingga CN : ND = 1 : 2. Titik P berada di rusuk DH sedemikian sehingga DP : PH = 2 : 1. Jika α adalah sudut antara bidang MNP dan garis PB maka nilai cos ⁡α = ….

  1. begin mathsize 14px style 5 over 44 square root of 44 end style

  2. begin mathsize 14px style 5 over 33 square root of 33 end style

  3. begin mathsize 14px style 5 over 22 square root of 22 end style

  4. begin mathsize 14px style 1 over 13 square root of 13 end style

  5. begin mathsize 14px style 1 over 11 square root of 11 end style

Iklan

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Iklan

Pembahasan

begin mathsize 14px style bold I bold. bold space bold ILUSTRASI bold space bold GAMBAR bold space bold KUBUS bold space bold SEPERTI bold space bold SOAL    bold I bold. bold space bold Identifikasi bold space bold sisi bold minus bold sisi bold space bold kubusnya end style

begin mathsize 14px style Dari space gambar space disamping comma space dapat space ditunjukkan space sebuah space kubus. space Kita space misalkan space rusuk space kubus space adalah space  3 straight a space left parenthesis untuk space mempermudah space proses space perhitungan right parenthesis comma space sehingga space sisi space colon space AM space equals space CN equals space PH equals space straight a  MD equals space ND space equals space DP space equals space 2 straight a..  Diperoleh space dari space MP equals square root of left parenthesis MD squared plus DP squared right parenthesis end root equals square root of left parenthesis left parenthesis 2 straight a right parenthesis squared plus left parenthesis 2 straight a right parenthesis squared right parenthesis end root equals 2 straight a square root of 2  Sehingga space panjang space rusuk space pada space segitiga space MNP space adalah space 2 straight a square root of 2  PQ space adalah space garis space tinggi space segitiga space sama space sisi space MNP. space Tinggi space segitiga space sama space sisi space MP space adalah  PQ space equals 1 half square root of 3.2 straight a square root of 2 equals space straight a square root of 6 end style

begin mathsize 14px style BD space adalah space diagonal space alas space kubus space yang space dirumuskan comma space space BD equals space rusuk space kubus space. space √ left parenthesis 2 space right parenthesis space equals space 3 straight a space √ left parenthesis 2 space right parenthesis comma space  rightwards arrow BQ space adalah space 2 over 3 space diagonal space rightwards arrow space BQ space equals space 2 over 3 diagonal space equals space 2 over 3.3 straight a space square root of 2 space equals space 2 straight a square root of 2  Panjang space BP space dapat space ditentukan space pada space segitiga space BDP comma space yaitu  BP space equals space square root of BP squared plus DP squared end root equals straight space square root of left parenthesis 3 straight a square root of 2 straight space end root right parenthesis straight space squared plus left parenthesis 2 straight a right parenthesis squared end root equals straight space square root of 18 straight a straight space squared plus 4 straight a squared end root equals straight a straight space square root of 22 straight space end root straight space  end style

begin mathsize 14px style Perhatikan space segitiga space BPQ comma space sehingga space kita space dapat space menentukan space nilai space cos space straight x space nya comma  yaitu space menggunakan space aturan space cosinus space colon  Cos space straight x space equals space fraction numerator BP squared plus PQ squared minus BQ squared over denominator 2 straight space BP. PQ end fraction equals straight space fraction numerator open parentheses straight a square root of 22 straight space end root close parentheses squared plus left parenthesis straight a square root of 6 straight space end root right parenthesis squared minus open parentheses 2 straight a square root of 2 straight space end root straight space close parentheses squared over denominator 2. straight space open parentheses straight a square root of 22 straight space end root close parentheses straight space. left parenthesis straight a square root of 6 straight space end root right parenthesis end fraction equals fraction numerator 22 straight a squared plus 6 straight a squared minus 8 straight a squared over denominator 2 straight a squared square root of 132 straight space end root straight space end fraction  space space space space space space space space space space space equals space fraction numerator 10 over denominator 2 square root of 33 straight space end root straight space end fraction equals fraction numerator 5 over denominator square root of 33 straight space end root straight space end fraction left parenthesis pembilang space dan space penyebut space dikalikan space √ left parenthesis 33 space right parenthesis right parenthesis comma space maka space hasilnya  space space space space space space space space space space equals fraction numerator 5 square root of 33 straight space end root over denominator 33 straight space end fraction end style

 

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

20

Iklan

Iklan

Pertanyaan serupa

Perhatikan limas di samping. Nilai kosinus sudut antara rusuk TA dan TC adalah ...

5

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia