math
posted by mohib .
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

So we have a rightangled triangle with angles 306090
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