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Pada suat segitiga PQR, diketahui, PQ = 2 5 ​ , RQ = 3 3 ​ serta ∠ P = 6 0 ∘ . Jika cos R = n m ​ , maka nilai dari m + n adalah ....

Pada suat segitiga PQR, diketahui,  serta . Jika , maka nilai dari  adalah ....

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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nilai dari .

nilai dari table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n end cell equals 5 end table.

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Ingat bahwa, pada aturan cosinus berlaku , sehingga Melalui aturan cosinus, diperoleh Oleh karena itu, nilai dari .

Ingat bahwa, pada aturan cosinus berlaku c squared equals a squared plus b squared minus 2 a b cos angle c, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell R Q squared end cell equals cell P Q squared plus P R squared minus 2 P Q times P R space cos space angle P end cell row cell open parentheses 3 square root of 3 close parentheses squared end cell equals cell open parentheses 2 square root of 5 close parentheses squared plus P R squared minus 2 cross times 2 square root of 5 cross times P R cross times cos space 60 degree end cell row 27 equals cell 20 plus P R squared minus 4 square root of 5 P R cross times 1 half end cell row 7 equals cell P R squared minus 2 square root of 5 P R end cell row cell Misal colon x end cell equals cell P R comma space maka end cell row cell straight x squared minus 2 square root of 5 straight x minus 7 end cell equals 0 row cell straight x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction end cell row blank equals cell fraction numerator 2 square root of 5 plus-or-minus square root of 20 plus 28 end root over denominator 2 end fraction end cell row blank equals cell square root of 5 plus-or-minus 2 square root of 3 end cell row blank rightwards arrow cell PR equals square root of 5 plus 2 square root of 3 end cell end table

Melalui aturan cosinus, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space angle R end cell equals cell fraction numerator R Q squared plus R P squared minus P Q squared over denominator 2 R Q times R P end fraction end cell row blank equals cell fraction numerator 27 plus open parentheses square root of 5 plus 2 square root of 3 close parentheses squared minus 20 over denominator 2 open parentheses 3 square root of 3 close parentheses open parentheses square root of 5 plus 2 square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 7 plus 5 plus 12 plus 4 square root of 15 over denominator 6 square root of 15 plus 36 end fraction end cell row blank equals cell fraction numerator 24 plus 4 square root of 15 over denominator 36 plus 6 square root of 15 end fraction end cell row blank equals cell fraction numerator 4 left parenthesis 6 plus square root of 15 right parenthesis over denominator 6 left parenthesis 6 plus square root of 15 right parenthesis end fraction end cell row blank equals cell 2 over 3 end cell row blank rightwards arrow cell m plus n equals 2 plus 3 end cell row blank equals 5 end table

Oleh karena itu, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n end cell equals 5 end table.

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