大师作文网求圆弧的面积,已知弦长3.89,弓形高0.72,求弓形面积?
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求圆弧的面积,已知弦长3.89,弓形高0.72,求弓形面积?
弦长L=3.89 弓形高H=0.72 半径R 圆心角α
(R-H)²+(L/2)²=R²
-2RH+H²+L²/4=0
R=(H²+L²/4)/(8H)=(0.72²+3.89²)/4/(2*0.72)=2.987100694
α=2arcsin(L/(2R))=2arcsin(3.89/(2*2.987100694))=1.41815276=81.25417°
扇形面积=R²*α/2=2.987100694²*1.41815276/2=6.326925845
三角形面积=R²sinα/2=2.987100694²sin1.41815276/2=4.40951085
弓形面积=扇形面积-三角形面积=6.326925845-4.40951085=1.917414996
(R-H)²+(L/2)²=R²
-2RH+H²+L²/4=0
R=(H²+L²/4)/(8H)=(0.72²+3.89²)/4/(2*0.72)=2.987100694
α=2arcsin(L/(2R))=2arcsin(3.89/(2*2.987100694))=1.41815276=81.25417°
扇形面积=R²*α/2=2.987100694²*1.41815276/2=6.326925845
三角形面积=R²sinα/2=2.987100694²sin1.41815276/2=4.40951085
弓形面积=扇形面积-三角形面积=6.326925845-4.40951085=1.917414996