Let the length of the diagonal BD = X cm, then, by condition, the length of the diagonal AC = BD / 2 = X / 2.
The diagonals of the rhombus, at the point of their intersection, are divided in half, then the length of the segment BO = BD / 2 = X / 2, and the length of the segment AO = AC / 2 = (X / 2) / 2 = X / 4.
Since the diagonals of the rhombus intersect at right angles, the triangle AOB is rectangular.
In a right-angled triangle, the tangent of the angle is equal to the ratio of the opposite leg to the adjacent leg.
tgbao = tgbac = BO / AO = (X / 2) / (X / 4) = 2.
Answer: The tangent of the angle BAC is 2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.