1) triangle area S= 1/2absinC can get ab=4 ①.

According to cosine theorem: C? =a？ +b？ -2abcosC

Get an a? +b？ =8 ②

Through ① ②, two equations can be solved:

a=2，b=2

2) According to sine theorem: a/sinA=b/sinB

∵sinA=2sinB, a=2b into the above formula.

Angle C = 60

Triangle ABC is a right triangle.

The area of triangle ABC is 1.

2. Solution:

1) can be obtained from sine theorem:

a/sinA=b/sinB=c/sinC

sinA+sinB=√2sinC

So a+b=√2c

a+b+c=2√2+2

So √2c+c=2√2+2.

So AB=c=2

2)a+b=√2c=2√2

S= 1/2absinC=(2-√2)sinC

ab=4-2√2

(a+b)^2=a^2+b^2+2ab=8

So a 2+b 2 = 4 √ 2.

cosC=(a^2+b^2-c^2)/2ab=√2/2

C=45