证明三角形的面积公式：S=(1/2)*a^2*[(sinBsinC)/sinA]

证明三角形的面积公式：S=(1/2)*a^2*[(sinBsinC)/sinA]
证明三角形的面积公式：S=(1/2)*a^2*[(sinBsinC)/sinA]

证明三角形的面积公式：S=(1/2)*a^2*[(sinBsinC)/sinA]
由正弦定理得
sinB=b*(sinA/a)
sinC=c*(sinA/a)
代入得
(1/2)*a^2*[(sinBsinC)/sinA]
=(1/2)*a^2*[(sinA*bc)/a^2]
=(1/2)*bc*sinA=S
所以
S=(1/2)*a^2*[(sinBsinC)/sinA]