# The greater base of an isosceles trapezoid is 2.9 dm, the acute angle is 45 degrees. the lateral sides of this trapezoid

The greater base of an isosceles trapezoid is 2.9 dm, the acute angle is 45 degrees. the lateral sides of this trapezoid are extended to their mutual intersection at point d. calculate the length of the perpendicular dropped from point d to the given base of the trapezoid

Let us draw the required height DH. Since DH is perpendicular to AE, the triangle DH is NOT rectangular.

According to the condition, the angle at a larger base is 45, then the angle NDE = 180 – 90 – 45 = 45, and therefore the triangle HDE is isosceles, DH = EH.

Since the angles at the base of an isosceles trapezoid are equal, then the angle BAE = CEA = 45, and then the triangle ADE is isosceles, then the height DH is also the median of the triangle, and then EH = AH = AE / 2 = 2.9 / 2 = 1.45 dm. Then DH = EH = 1.45 dm.

Answer: The height is 1.45 dm. 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.