Bantu jawab yaa. pada segitiga ABC diketahui cos A=8/17 dan sin B=5/13. nilai tan C

Kelas 11 Matematika
Bab Trigonometri Lanjut

cos A = 8/17 → x/r

y = √(r² - x²)
y = √(17² - 8²)
y = √(289 - 64)
y = √(225)
y = 15

sin A = y/r
sin A = 15/17

sin B = 5/13 → y/r

x = √(r² - y²)
x = √(13² - 5²)
x = √(169 - 25)
x = √144
x = 12

cos B = 12/13

Sudut A + sudut B + sudut C = 180°
A + B = 180° - C
sin (A + B) = sin (180° - C)
sin A cos B + cos A sin B = sin C
15/17 . 12/13 + 8/17 . 5/13 = sin C
180/221 + 40/221 = sin C
sin C = 220/221 → y/r

x = √(r² - y²)
x = √(221² - 220²)
x = √48.841 - 48.400)
x = √441
x = 21

tan C = y/x
tan C = 220/21

Cos A = 8/17
tan A = 15/8

sin B = 5/13
tan B = 5/12

tan C = tan (A+B)
= \frac{ \frac{15}{8} + \frac{5}{12} }{1 - \frac{15}{8} \frac{5}{12} }
= \frac{ \frac{220}{96} }{ \frac{21}{96} }
= \frac{220}{21}

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