水库大坝的横截面是梯形ABCD坝顶AD =6 坡长CD=8 坡底BC=30°

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  • 作DE⊥BC,AF⊥BC,垂足分别为E、F,角C=180°-角ADC=45°,

    △DEC是等腰RT△,

    DE=CD*sin45°=4√2,

    CE=DE=4√2,

    EF=AD=6,

    BF=BC-CE-EF=30-6-4√2=24-4√2,

    tanB=AF/BF=4√2/(24-4√2)=(3√2+1)/17,角B=arctan[(3√2+1)/17],

    ∴角ABC≈17°8'

    S梯形ABCD=(AD+BC)*DE/2=(6+30)*4√2/2=72√2,

    ∴土石料的体积V=72√2*100=7200√2≈10182.338