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Dalam segitiga PQR diketahui cos P=21​2​ dan cos Q=21​3​. Nilai cos R= ...

Pertanyaan

Dalam segitiga PQR diketahui cos space straight P equals 1 half square root of 2 dan cos space straight Q equals 1 half square root of 3. Nilai cos space straight R equals ...

  1. 1 fourth square root of 2 open parentheses 1 plus square root of 3 close parentheses

  2. 1 fourth square root of 2 open parentheses 1 minus square root of 3 close parentheses

  3. 1 fourth square root of 2 open parentheses square root of 3 minus 1 close parentheses

  4. 1 half square root of 2 open parentheses 1 minus square root of 3 close parentheses

  5. 1 half square root of 2 open parentheses square root of 3 minus 1 close parentheses 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui:

cos space straight P equals 1 half square root of 2 rightwards arrow straight P equals 45 degree
cos space straight Q equals 1 half square root of 3 rightwards arrow straight Q equals 30 degree

Ditanya:

cos space straight R

Perlu diingat bahwa:

cos space left parenthesis straight A plus straight B right parenthesis equals cos space straight A space cos space straight B minus sin space straight A space sin space straight B 

Kita tahu jumlah sudut dalam segitiga adalah 180 degree, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P plus straight Q plus straight R end cell equals cell 180 degree end cell row cell 45 degree plus 30 degree plus straight R end cell equals cell 180 degree end cell row cell 75 degree plus straight R end cell equals cell 180 degree end cell row straight R equals cell 180 degree minus 75 degree end cell row straight R equals cell 105 degree end cell end table

Dengan menggunakan rumus di atas nilai dari cos space straight R dapat ditentukan seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis straight A plus straight B right parenthesis end cell equals cell cos space straight A times cos space straight B minus sin space straight A times sin space straight B end cell row cell cos space open parentheses 60 degree plus 45 degree close parentheses end cell equals cell cos space 60 degree times cos space 45 degree minus sin space 60 degree times sin space 45 degree end cell row blank equals cell 1 half times 1 half square root of 2 minus 1 half square root of 3 times 1 half square root of 2 end cell row blank equals cell 1 fourth square root of 2 minus 1 fourth square root of 6 end cell row blank equals cell 1 fourth square root of 2 open parentheses 1 minus square root of 3 close parentheses end cell end table

Sehingga, nilai cos space straight R adalah 1 fourth square root of 2 open parentheses 1 minus square root of 3 close parentheses.

Jadi, jawaban yang tepat adalah B.

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