正弦余弦定理和解斜三角形

1.2/sin45 = b/sinB = 2√2
sinB = b/2√2 有两解,说明B在90到135之间有一解,
√2/2 < b/2√2 < 1 ==> 2 < b < 2√2
2.tanA>0,tanB>0,tanC>0
由tanA > 0==> t>-1;
由tanB > 0==> t>1;
由tanC = -tan(A+B) = - (tanA + tanB)/(1- tanAtanB)
= - 2t/(2-t^2) > 0
t > 1,所以 -2t < 0 所以2 - t^2 < 0 ==>t > √2
==> t>√2