Segitiga ABC dengan a + b = 10 satuan. Besar sudut A = 30° dan sudut B = 45°. Panjang sisi b adalah .... satuan. a. 5(√2 - 1) b. 5(2 - √2) c. 10(2 - √2) d. 10(

a/sinA = b/sinB
a/sin30 = b/sin45
a/½ = b/½√2
a = b/√2 = ½b√2

a + b = 10
½b√2 + b = 10
b (½√2 + 1) = 10
b = 10/(½√2 + 1)
b = (5√2 - 10)/(-½) = 10(2-√2)

a = 10-b
a / sin A = b / sin B
(10-b) / sin 30 = b / sin 45
(10-b) / (1/2) = b / (√2/2)
(10-b) × (√2/2) = (1/2) × b
-------------------------------------- × 2
(10 - b)√2 = b
10√2 - b√2 = b
10√2 = b√2 + b
b√2 + b = 10√2
b(√2+1) = 10√2
b = 10√2 / (√2+1)
b = {10√2 / (√2+1)} × {(√2-1) / (√2-1)}
b = 10√2(√2-1) / 2-1
b = 10(2 - √2)