Find the diagonals of the rectangle ABCD, if the angle CAD = 30 degrees, CD = 4cm.

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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