Pertanyaan

Tentukan nilai x dan α pada gambar berikut. (Gunakan kalkulator untuk menentukan nilai )

Tentukan nilai $x$ dan $α$ pada gambar berikut.
(Gunakan kalkulator untuk menentukan nilai )

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh nilai .

diperoleh nilai

Pembahasan

Selanjutnya ditentukan besar sudut sebagai berikut. Dengan demikian diperoleh nilai .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space B end cell equals cell fraction numerator D C over denominator x end fraction end cell row x equals cell fraction numerator 6 square root of 3 over denominator sin space 60 degree end fraction end cell row blank equals cell fraction numerator 6 square root of 3 over denominator begin display style 1 half end style square root of 3 end fraction end cell row x equals 12 row cell B C end cell equals cell square root of x squared minus D C squared end root end cell row blank equals cell square root of 12 squared minus open parentheses 6 square root of 3 close parentheses squared end root end cell row blank equals cell square root of 144 minus 108 end root equals square root of 36 end cell row blank equals 6 row cell A C end cell equals cell 20 plus 6 end cell row blank equals 26 row cell A D end cell equals cell square root of A C squared plus D C squared end root end cell row blank equals cell square root of 26 squared plus open parentheses 6 square root of 3 close parentheses squared end root end cell row blank equals cell square root of 676 plus 108 end root end cell row blank equals cell square root of 784 end cell row blank equals 28 end table end style$

Selanjutnya ditentukan besar sudut sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B D squared end cell equals cell A B squared plus A D squared minus 2 open parentheses A B close parentheses open parentheses A D close parentheses space cos space alpha end cell row cell 12 squared end cell equals cell 20 squared plus 28 squared minus 2 open parentheses 20 close parentheses open parentheses 28 close parentheses space cos space alpha end cell row 144 equals cell 400 plus 784 minus 1.120 space cos space alpha end cell row 144 equals cell 1.184 minus 1.120 space cos space alpha end cell row cell cos space alpha end cell equals cell fraction numerator 1.184 minus 144 over denominator 1.120 end fraction end cell row cell cos space alpha end cell equals cell 0 comma 928571 end cell row alpha equals cell arccos space open parentheses 0 comma 928571 close parentheses end cell row blank equals cell 21 comma 79 degree end cell end table end style$

Dengan demikian diperoleh nilai .