Diketahui segitiga ABC siku-siku di C. Jika sin(A-B) = 5a, sinA . Sin B = 2/5, maka a =...
Matematika
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Pertanyaan
Diketahui segitiga ABC siku-siku di C. Jika sin(A-B) = 5a, sinA . Sin B = 2/5, maka a =...
1 Jawaban
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1. Jawaban Anonyme
∆ABC siku di C
A + B = 90°
sin (A - B) = 5a
sin (A + B) = 1
---------------------- (+)
2 sin A cos B = 1 + 5a
cos (A + B) = 0
cos A cos B = sin A sin B = 2/5
tan A tan B = 1
2 sin A cos B = 1 + 5a
Kedua ruas (: cos A cos B)
2 . tan A tan B = (1 + 5a)/(2/5)
2 . 1 = (1 + 5a) × 5/2
1 + 5a = 2 × 2/5
5a = 4/5 - 1
5a = -1/5
a = -1/25