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In rectangle ABCD, shown here, ACB measures 30° and. CD = 40 mm. What is the area of rectangle ABCD? Express your answer as a decimal to the nearest tenth

  • math -

    So we have a right-angled triangle with angles 30-60-90
    The sides of such a triangle are in the ration 1 : √3 : 2
    So ours must have sides 40,40√3, and 80
    making the base 80
    Area = 40(40√3) = 1600√3 = appr. 2771.3

    or

    tan30 =AB/BC
    BC = 40/tan30 = 69.282
    area = 40(69.282) = appr. 2771.3

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