Roboguru

Ubahlah ke sudut lancip, kemudian tentukan nilainya: b.

Pertanyaan

Ubahlah ke sudut lancip, kemudian tentukan nilainya:

b. begin mathsize 14px style tan space 60 degree end style 

Pembahasan Soal:

Sudut lancip adalah sudut yang ada pada kuadran I.

 undefined ada pada kuadrat I.

Dengan tabel nilai trigonometri untuk sudut istimewa maka diperoleh:

undefined  

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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Pertanyaan yang serupa

Lengkapilah tabel berikut!

Pembahasan Soal:

  • cos space 60 degree equals 1 half 
     
  • tan space 60 degree equals fraction numerator begin display style 1 half end style square root of 3 over denominator begin display style 1 half end style end fraction equals square root of 3 
  • cosec space 60 degree equals fraction numerator 1 over denominator sin space 60 degree end fraction equals fraction numerator 1 over denominator begin display style 1 half square root of 3 end style end fraction times fraction numerator 2 square root of 3 over denominator 2 square root of 3 end fraction equals 2 over 3 square root of 3 
     
  • sec space 60 degree equals fraction numerator 1 over denominator cos space 60 degree end fraction equals fraction numerator 1 over denominator begin display style 1 half end style end fraction equals 2  
     
  • cot space 60 degree equals fraction numerator 1 over denominator tan space 60 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction equals 1 third square root of 3 

Jadi, tabel yang telah lengkap adalah sebagai berikut.


Roboguru

Perhatikan gambar segitiga siku-siku  di bawah. Tentukan: b. Luas segitiga .

Pembahasan Soal:

size 14px triangle size 14px A size 14px D size 14px C siku-siku di undefined 
size 14px triangle size 14px B size 14px D size 14px C siku-siku di size 14px D size 14px comma size 14px space size 14px angle size 14px C size 14px B size 14px D size 14px equals size 14px 30 size 14px degree size 14px space size 14px dan size 14px space size 14px angle size 14px D size 14px C size 14px B size 14px equals size 14px 60 size 14px degree 

Perbandingan segitiga siku-siku yang mempunyai sudut undefined adalah 

begin mathsize 14px style alas space colon space tinggi space colon space hipotenusa equals 1 space colon space square root of 3 space colon space 2 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator A D over denominator C D end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell fraction numerator 8 over denominator C D end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction space space space space space space space space end cell row cell C D end cell equals cell 8 cross times square root of 3 space space space space space space space space space end cell row blank equals cell 8 square root of 3 space cm end cell row blank blank blank row cell fraction numerator C D over denominator B D end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell fraction numerator 8 square root of 3 over denominator B D end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction space space space space space space space space end cell row cell B D end cell equals cell 8 square root of 3 cross times square root of 3 space space space space space space space space space end cell row blank equals cell 24 space cm end cell end table end style 

Dengan menggunakan rumus luas segitiga, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space capital delta A B C end cell equals cell 1 half cross times A B cross times C D end cell row blank equals cell 1 half cross times space left parenthesis 8 plus 24 right parenthesis space cm cross times 8 square root of 3 space cm end cell row blank equals cell fraction numerator 1 space over denominator 2 end fraction cross times 32 cross times 8 square root of 3 space cm squared end cell row blank equals cell 16 cross times 8 square root of 3 space cm squared end cell row blank equals cell 128 square root of 3 space cm squared end cell end table end style

Jadi, luas segitiga tersebut adalah Error converting from MathML to accessible text..

Roboguru

Tentukan luas persegi panjang  berikut.

Pembahasan Soal:

Dari gambar yang diberikan, dapat ditentukan:

space space space space cos space straight L equals KL over NL cos space 60 degree equals KL over 7 space space space space space space space space space 1 half equals KL over 7 space space space 2 cross times KL equals 1 cross times 7 space space space space 2 cross times KL equals 7 space space space space space space space space space space KL equals 7 over 2 

Maka:

KN equals square root of NL squared minus KL squared end root KN equals square root of 7 squared minus open parentheses 7 over 2 close parentheses squared end root KN equals square root of 49 minus 49 over 4 end root KN equals square root of fraction numerator 196 minus 49 over denominator 4 end fraction end root KN equals square root of 147 over 4 end root KN equals 1 half square root of 147 

Sehingga:

straight L subscript KLMN equals straight p cross times straight l straight L subscript KLMN equals KL cross times KN straight L subscript KLMN equals 7 over 2 cross times 1 half square root of 147 straight L subscript KLMN equals 7 over 4 square root of 147 

Jadi, luas persegi panjang KLMN tersebut adalah 7 over 4 square root of 147 space cm squared.

Roboguru

Lengkapilah tabel berikut!

Pembahasan Soal:

  • cos space 30 degree equals 1 half square root of 3 
  • table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 30 degree end cell equals cell fraction numerator sin space 30 degree over denominator cos space 30 degree end fraction equals fraction numerator 1 half over denominator 1 half square root of 3 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction equals 1 third square root of 3 end cell end table   
  • cosec space 30 degree equals fraction numerator 1 over denominator sin space 30 degree end fraction equals fraction numerator 1 over denominator begin display style 1 half end style end fraction equals 2 
  • sec space 30 degree equals fraction numerator 1 over denominator cos space 30 degree end fraction equals fraction numerator 1 over denominator begin display style 1 half square root of 3 end style end fraction times fraction numerator 2 square root of 3 over denominator 2 square root of 3 end fraction equals 2 over 3 square root of 3 
  • cot space 30 degree equals fraction numerator 1 over denominator tan space 30 degree end fraction equals fraction numerator 1 over denominator begin display style 1 third end style square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction equals square root of 3 

Jadi, tabel yang telah dilengkapi adalah sebagai berikut.


Roboguru

Perhatikan gambar berikut. Tentukan panjang CB dan AB, apabila diketahui panjang !

Pembahasan Soal:

Ingatlah perbandingan sisi (trigonometri) pada segitiga siku-siku, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space alpha end cell equals cell depan over miring end cell row cell cos space alpha end cell equals cell samping over miring end cell end table

Sehingga diperoleh:

  • Panjang CB

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight alpha end cell equals cell CB over AC end cell row cell cos space 30 degree end cell equals cell fraction numerator CB over denominator 12 square root of 3 space cm end fraction end cell row cell 1 half square root of 3 end cell equals cell fraction numerator CB over denominator 12 square root of 3 space cm end fraction end cell row cell 2 CB end cell equals cell 12 square root of 3 space cm cross times square root of 3 end cell row cell 2 CB end cell equals cell 36 space cm end cell row CB equals cell 36 over 2 end cell row CB equals cell 18 space cm end cell end table

  • Panjang AB

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space alpha end cell equals cell AB over AC end cell row cell sin space 30 degree end cell equals cell fraction numerator AB over denominator 12 square root of 3 space cm end fraction end cell row cell 1 half end cell equals cell fraction numerator AB over denominator 12 square root of 3 space cm end fraction end cell row cell 2 AB end cell equals cell 12 square root of 3 space cm end cell row AB equals cell fraction numerator 12 square root of 3 space cm over denominator 2 end fraction end cell row AB equals cell 6 square root of 3 space cm end cell end table

Maka, panjang CB dan AB adalah 18 space cm dan 6 square root of 3 space cm.

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