不规则形状计算
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不规则形状计算
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![不规则形状计算](/uploads/image/z/18747096-24-6.jpg?t=%E4%B8%8D%E8%A7%84%E5%88%99%E5%BD%A2%E7%8A%B6%E8%AE%A1%E7%AE%97)
已知弦长L=9.5米,拱高H=1.3米,求弧长C和面积S?
设弧半径为R,弧所对的圆心角为A.
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=1.3/2+9.5^2/(8*1.3)
=9.328米
A=2*arc sin((L/2)/R)
=2*arc sin((9.5/2)/9.328)
=61.22度
=61.22*PI/180
=1.068弧度
C=R*A=9.328*1.068=9.967米
S=π*R^2*A/2π-1/2*L*(R-H)
=R^2*A/2-1/2*L*(R-H)
=9.328^2*1.068/2-1/2*9.5*(9.328-1.3)
=8.33平方米
设弧半径为R,弧所对的圆心角为A.
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=1.3/2+9.5^2/(8*1.3)
=9.328米
A=2*arc sin((L/2)/R)
=2*arc sin((9.5/2)/9.328)
=61.22度
=61.22*PI/180
=1.068弧度
C=R*A=9.328*1.068=9.967米
S=π*R^2*A/2π-1/2*L*(R-H)
=R^2*A/2-1/2*L*(R-H)
=9.328^2*1.068/2-1/2*9.5*(9.328-1.3)
=8.33平方米