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Buktikan aturan cosinus dalam segitiga dengan menggunakan vektor.

Buktikan aturan cosinus dalam segitiga dengan menggunakan vektor.

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S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

di atas merupakan pembuktian aturan cosinus dalam segitiga dengan menggunakan vektor.

di atas merupakan pembuktian aturan cosinus dalam segitiga dengan menggunakan vektor.

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Pembahasan

Ingat kembali: Perhatikan gambar di bawah ini: Jadi, di atas merupakan pembuktian aturan cosinus dalam segitiga dengan menggunakan vektor.

Ingat kembali:

top enclose a times top enclose b equals open vertical bar top enclose a close vertical bar times open vertical bar top enclose b close vertical bar space cos space alpha

c with rightwards arrow on top times c with rightwards arrow on top equals open vertical bar c with rightwards arrow on top close vertical bar squared

cos space open parentheses 180 minus alpha close parentheses equals negative cos space alpha

Perhatikan gambar di bawah ini:

a with rightwards arrow on top plus b with rightwards arrow on top equals c with rightwards arrow on top Sehingga straight c with rightwards arrow on top times straight c with rightwards arrow on top equals open parentheses straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses open parentheses straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses open vertical bar straight c with rightwards arrow on top close vertical bar squared equals straight a with rightwards arrow on top times straight a with rightwards arrow on top plus 2 times straight a with rightwards arrow on top times straight b with rightwards arrow on top plus straight b with rightwards arrow on top times straight b with rightwards arrow on top open vertical bar straight c with rightwards arrow on top close vertical bar squared equals open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 times straight a with rightwards arrow on top times straight b with rightwards arrow on top open vertical bar straight c with rightwards arrow on top close vertical bar squared equals open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 times straight a with rightwards arrow on top times straight b with rightwards arrow on top open vertical bar straight c with rightwards arrow on top close vertical bar squared equals open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared plus 2 times open vertical bar straight a with rightwards arrow on top close vertical bar times open vertical bar straight b with rightwards arrow on top close vertical bar space cos space open parentheses 180 minus straight alpha close parentheses open vertical bar straight c with rightwards arrow on top close vertical bar squared equals open vertical bar straight a with rightwards arrow on top close vertical bar squared plus open vertical bar straight b with rightwards arrow on top close vertical bar squared minus 2 times open vertical bar straight a with rightwards arrow on top close vertical bar times open vertical bar straight b with rightwards arrow on top close vertical bar space cos space straight alpha 

Jadi, di atas merupakan pembuktian aturan cosinus dalam segitiga dengan menggunakan vektor.

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