A rectangle is a rectangle in which opposite sides are equal and all corners are right. The diagonals of the rectangle are equal to each other:
AC = BD.
Since the diagonal of the rectangle divides it into two equal right-angled triangles, to calculate AC, consider the triangle ΔАСD.
Since the angle ∠CAD and the leg opposite to it are known, it is most convenient to apply the theorem of sines:
sin CAD = CD / AC;
AC = CD / sin CAD;
sin 30º = 1/2 = 0.5;
AC = 4 / 0.5 = 8 cm.
Answer: The length of the AC diagonal is 8 cm.
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