Question

Diket segitiga ABC dgn sudut A = 60, sudut C = 75, sudut B = 45 drjat, lalu panjang AC = 8 cm. Berapa panjang AB dan BC?

Answer 1

Diket segitiga ABC dgn sudut A = 60, sudut C = 75, sudut B = 45 drjat, lalu panjang AC = 8 cm. Berapa panjang AB dan BC?

AC = b
AB = c
BC = a

a/sin a = b/sin b = c/sin c

a/sina = b/sin b
a/sin 60° = 8/sin 45°
a×sin 45° = 8×sin 60°
a × √2/2 =8 × √3/2
a = 4√6 cm

jadi panjang BC = 4√6 cm

a/sina = c/sin c
4√6/sin 60° = c/sin 75°
4√6×sin 75° = c×sin 60°
c × √3/2 =  4√6 × sin 75°
c = (8√2 × sin 75°) cm
jadi panjang garis AB adalah (8√2 × sin 75°) cm