From the point of intersection of the diagonals of the rhombus, a perpendicular is drawn, which divides the side

From the point of intersection of the diagonals of the rhombus, a perpendicular is drawn, which divides the side of the rhombus into segments 18 cm and 32 cm long. Find the tangent of the angle formed by the side of the rhombus and the smaller diagonal.

The diagonals of the rhombus intersect at point O at a right angle, then the triangle AOB is rectangular. OH is the height of a right-angled triangle drawn from the vertex of the right angle to the hypotenuse.

Then, by the property of this height: OH ^ 2 = AH * BH = 32 * 18 = 576. OH = 24 cm.

In the right-angled triangle ВOН, we define the tangent of the angle OВН.

tgBOH = OH / BH = 24/18 = 4/3 = 1 (1/3).

Answer: The tangent of the angle is 1 (1/3).