In an isosceles trapezoid, the diagonal is 26 cm, the height is 10 cm, and the upper base is 14 cm

| February 5, 2021 | education

In an isosceles trapezoid, the diagonal is 26 cm, the height is 10 cm, and the upper base is 14 cm. At what angle is the side inclined?

To solve this problem, we need to use the formula for the diagonal of an isosceles trapezoid, based on the data we know, we can only use this formula: d = √ (h ^ 2 + (b + h * ctg a) ^ 2), where: d is the diagonal, h – height, b – upper base, a – angle of inclination of the side. Substituting the available data into the formula, we get: 26 = √ (10 ^ 2 + (14 + 10 * ctg a) ^ 2). Next, we need to solve the equation in which the unknown is ctg a. 676 = 100 + (14 + 10 * ctg a) ^ 2.576 = (14 + 10 * ctg a) ^ 2.√ 576 = 14 + 10 * ctg a 24 = 14 + 10 * ctg a. 10 = 10 * ctg a. ctg a = 1. Using the data given in the table of sines, cosines, tangents and cotangents, we see that ctg 45 = 1.
Answer: 45 degrees



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.