segitiga abc semua sudutnya lancip dengan sin A = 8/10 Sin B = 5/13. Tentukan cos A - B

Diketahui:

Jika
[tex] \sin(A) = \frac{8}{10} [/tex]
maka:
[tex] \cos(A) = \frac{ {10}^{2} - {8}^{2} }{10} = \frac{6}{10} [/tex]

Jika
[tex] \sin(B) = \frac{5}{13} [/tex]
maka
[tex] \cos(B) = \frac{ {13}^{2} - {5}^{2} }{13} = \frac{12}{13} [/tex]
sehingga

[tex]cos (A - B) = \cos(A) \cos(B) + \sin(A) \sin(B) \\ = \frac{6}{10} \times \frac{12}{13} + \frac{8}{10} \times \frac{5}{13} \\ = \frac{72 + 40}{130} \\ = \frac{112}{130} [/tex]