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Dalam suatu segitiga ABC diketahui cos ∠A=53​ dan cos ∠B=135​. Nilai  sin ∠C = ...

Pertanyaan

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

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

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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