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余弦定理求BC,正弦定理求sinA
(1)BC²=AB²+AC²-2AB.ACcosBAC
=2²+1²-2×2×1cos120°=4+1+4cos60°=7,BC=√7
BD=√7/3,CD=2√7/3
sinA/BC=sinB/AC,sinB=sinA.AC/BC=sin120°×1/√7=√3/2÷√7=√3/2√7
=√21/14
(2)余弦定理求AD,余弦定理求cos∠BDA
AD.BC=|AD|.|BC|cos∠BDA