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Diketahui segitiga ABC siku-siku di C,  dan . Tentukan nilai !

Pertanyaan

Diketahui segitiga ABC siku-siku di C, begin mathsize 14px style sin space A space sin space B equals 2 over 5 end style dan size 14px sin size 14px space size 14px A size 14px space size 14px cos size 14px space size 14px B size 14px minus size 14px cos size 14px space size 14px A size 14px space size 14px sin size 14px space size 14px B size 14px equals size 14px 5 size 14px a. Tentukan nilai begin mathsize 14px style a end style!

Pembahasan Soal:

Diketahui: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space A space sin space B end cell equals cell 2 over 5 end cell row cell sin space A space cos space B minus cos space A space sin space B end cell equals cell 5 a end cell row cell sin space left parenthesis A minus B right parenthesis end cell equals cell 5 a end cell end table end style 

Segitiga di atas dapat digambar sebagai berikut.

Berdasarkan gambar di atas diperoleh hubungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space A end cell equals cell fraction numerator B C over denominator A B end fraction equals cos space B end cell row cell sin space B end cell equals cell fraction numerator A C over denominator A B end fraction equals cos space A end cell end table end style 

sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space A space sin space B end cell equals cell 2 over 5 end cell row cell cos space B space cos space A end cell equals cell 2 over 5 end cell row cell cos space A space cos space B end cell equals cell 2 over 5 end cell end table end style 

sehingga dapat ditentukan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis A minus B right parenthesis end cell equals cell cos space A space cos space B plus sin space A space sin space B end cell row blank equals cell 2 over 5 plus 2 over 5 end cell row blank equals cell 4 over 5 end cell end table end style 

Karena begin mathsize 14px style sin squared theta plus cos squared theta equals 1 end style maka dapat ditentukan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 1 equals cell sin squared space open parentheses A minus B close parentheses plus cos squared space left parenthesis A minus B right parenthesis end cell row 1 equals cell open parentheses 5 a close parentheses squared plus open parentheses 4 over 5 close parentheses squared end cell row 1 equals cell 25 a squared plus 16 over 25 end cell row cell 25 a squared end cell equals cell 1 minus 16 over 25 end cell row blank equals cell 9 over 25 end cell row cell a squared end cell equals cell 9 over 625 end cell row a equals cell square root of 9 over 625 end root end cell row a equals cell 3 over 25 end cell end table end style

Dengan demikian, diperoleh nilai undefined adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 25 end cell end table end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 April 2021

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