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Diketahui  dan  ( dan  sudut lancip). Nilai  = ...

Diketahui sin space straight alpha equals 3 over 5 dan cos space straight beta equals 12 over 13 (straight alpha dan straight beta sudut lancip). Nilai sin space left parenthesis straight alpha plus straight beta right parenthesis = ...

  1. 56 over 65 

  2. 20 over 65 

  3. 48 over 65 

  4. 16 over 65 

  5. 36 over 65 

Jawaban:

Diketahui : sin space straight alpha equals 3 over 5cos space straight beta equals 12 over 13 

Ingat kembali bahwa sin space straight alpha equals depan over miring dan cos space straight alpha equals samping over miring maka

sin space straight alpha equals 3 over 5 equals depan over miring equals straight a over straight c 

Kita dapat mencari nilai b (sisi samping) untuk mencari nilai cos space straight alpha dengan teorema pythagoras pada segitiga yaitu straight a squared plus straight b squared equals straight c squared sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a squared plus straight b squared end cell equals cell straight c squared end cell row cell 3 squared plus straight b squared end cell equals cell 5 squared end cell row cell straight b squared end cell equals cell 5 squared minus 3 squared end cell row straight b equals cell square root of 5 squared minus 3 squared end root end cell row straight b equals cell square root of 25 minus 9 end root end cell row straight b equals cell square root of 16 end cell row straight b equals 4 end table 

cos space straight alpha equals samping over miring equals straight b over straight a equals 4 over 5 

Selanjutnyaspace 

cos space straight beta equals 12 over 13 equals samping over miring equals straight b over straight c 

Kita dapat mencari nilai a (sisi depan) untuk mencari nilai sin space straight beta dengan teorema pythagoras pada segitiga yaitu straight a squared plus straight b squared equals straight c squared sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a squared plus straight b squared end cell equals cell straight c squared end cell row cell straight a squared plus 12 squared end cell equals cell 13 squared end cell row cell straight a squared end cell equals cell 13 squared minus 12 squared end cell row straight a equals cell square root of 13 squared minus 12 squared end root end cell row straight a equals cell square root of 169 minus 144 end root end cell row straight a equals cell square root of 25 end cell row straight a equals 5 end table

sin space straight beta equals depan over miring equals straight a over straight c equals 5 over 13   

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space left parenthesis straight alpha plus straight beta right parenthesis end cell equals cell sin space straight alpha space cos space straight beta plus cos space straight alpha space sin space straight beta end cell row blank equals cell 3 over 5 cross times 12 over 13 plus 4 over 5 cross times 5 over 13 end cell row blank equals cell 36 over 65 plus 20 over 65 end cell row blank equals cell 56 over 65 end cell end table 

Oleh karena itu, jawaban yang benar adalah A.space 

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