Дано трапеция ABCD , AD || BC, AD =10 , BC =6 ,∠A =90° , ∠CAD =∠30°.
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а) AB*BC -? б) AC*AD -? в) BC*DA -?
а)
AB*BC=|AB|*|BC|*cos∠(AB,BC) =|AB|*|BC|*cos90° =|AB|*|BC|*0 =0 .
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б)
AC*AD =|AC|*|AD|*cos∠(AC,AD) =*|BC|/sin60°*|AD|*cos30°=
BC|*|AD|*(cos30°/sin60°)= BC|*|AD|=6*10 =60.
* * * ∠(AC,AD) = ∠BAC= ∠A -∠CAD =90°-30° =60° * * *
* * * cos30°=sin60° =√3/2 * * *
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в)
BC*DA =|BC|*DA|*cos∠(BC,DA) =6*10*cos180° =60*(-1) = - 60.