In the ABCD rectangle, the abAB side is 12 cm and the ADD angle is 60 degrees, find the AC diagonal.

A rectangle is a quadrangle in which all angles are right and equal to each other.

In order to find the length of the diagonal AC, consider the triangle ΔABD. This triangle is rectangular. To calculate the length of the diagonal BD, we use the cosine theorem. The cosine of an acute angle in a right triangle is the ratio of the adjacent leg to the hypotenuse:

cos α = AB / BD;

BD = AB / cos α;

cos 60 ° = 1/2 = 0.5;

BD = 12 / 0.5 = 24 cm.

Answer: The length of the AC diagonal is 24 cm.