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