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Dalam suatu segitiga ABC diketahui dan Nilai

Dalam suatu segitiga ABC diketahui cos space angle A equals 3 over 5 dan cos space angle B equals 5 over 13. spaceNilai space sin space angle C space equals space...

  1. 56 over 65

  2. 33 over 65

  3. negative 16 over 65

  4. negative 33 over 65

  5. negative 56 over 65

Jawaban:

Dalam suatu segitiga ABC diketahui cos space angle A equals 3 over 5 space d a n space cos space angle B equals 5 over 13

Rumus identitas trigonometri = sin squared A plus cos squared A equals 1

cos space angle A equals 3 over 5  sin squared A plus cos squared A equals 1  sin squared A plus open parentheses 3 over 5 close parentheses squared equals 1  sin squared A plus 9 over 25 equals 1  sin squared A equals 1 minus 9 over 25  sin squared A equals fraction numerator 25 minus 9 over denominator 25 end fraction  sin squared A equals 16 over 25  sin space A equals 4 over 5    cos angle B equals 5 over 13  sin squared B plus cos squared B equals 1  sin squared B plus open parentheses 5 over 13 close parentheses squared equals 1  sin squared B plus 25 over 169 equals 1  sin squared B equals 1 minus 25 over 169  sin squared B equals fraction numerator 169 minus 25 over denominator 25 end fraction  sin squared B equals 144 over 25  sin space B equals 12 over 5

Nilai dari sudut C

angle A plus angle B plus angle C equals 180 to the power of 0  sin angle C equals sin left parenthesis 180 to the power of 0 minus open square brackets angle A plus angle B close square brackets right parenthesis  sin angle C equals sin space 180 to the power of 0 space cos space open parentheses angle A plus angle B close parentheses minus cos space 180 to the power of 0 space sin space open parentheses angle A plus angle B close parentheses  sin angle C equals sin open parentheses angle A plus angle B close parentheses  sin angle C equals sin space angle A space cos angle B plus cos space angle A space sin space angle B  sin angle C equals open parentheses 4 over 5 close parentheses open parentheses 5 over 13 close parentheses plus open parentheses 3 over 5 close parentheses open parentheses 12 over 12 close parentheses  sin angle C equals 56 over 65

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