Question

Pada segitiga ABC diketahui a+b = 12. Jika <A = 60° , <B = 45°, panjang sisi b = ....
a. 3
b. 2(√3 + √2)
c. 12√6 - 24
d. 6√6 - 12
e. 3 - √6

beserta caranya ya kak!!

Answer 1

A + b = 12
a = 12 - b

sinA / a = sinB / b
sin60 / a = sin45 / b
sin60 / (12 - b) = sin45 / b
(1/2√3) / (12 - b) = (1/2√2) / b

6√2 - 1/2√2b = 1/2√3b
6√2 - 1/2√2b - 1/2√3b = 0
-1/2√2b - 1/2√3b = -6√2
1/2√2b + 1/2√3b = 6√2
(1/2√2 + 1/2√3)b = 6√2
b =            6√2____
         1/2√2 + 1/2√3

b = 6√2 / ((√2 + √3) /2)
b = 12√2 / (√2 + √3)
b = (12√2)(√2) + (12√2)(-√3) / (2 - 3)
b = (24 - 12√6) / -1
b = -24 + 12√6
b = 12√6 - 24
---> C.