1.
A=arctan(3/5) B=arctan(1/4)
C=π-A-B=π-arctan(3/5)-archtan(1/4)=135°
三角形内角正弦之比=他们的对边边长之比.
3/5>1/4 所以tanA>tanB,由tan函数在(0,π/2)的单调性可知 A>B
所以sinA>sinB,最短边是b,最长边是c,c=1
c/sinC = b/sinB
b=c*sinB/sinC = 0.343
2.a b c 分别是A B C的对边吗?
设角BAC=θ
a/sinA = b/sinB = c/sinC
所以 4/sinθ=1/sin(π-2θ)
sinθ=4sin(π-2θ)
sinθ=4sin(2θ)=8sinθcosθ
所以sinθ=0 或cosθ=1/8
所以θ=0（舍去）或θ=82.82°
角BAD=角DAC=θ/2
角ADC=180-(角DAC+角ACD)=180-3θ/2
b/sin∠ADC = AD/sinC
AD=b*sinθ/sin(180-3θ/2)
AD=1*sinθ/sin(3θ/2) = 1.2