From a point located at a distance of 6 cm from the plane, two inclined ones are drawn. Find the distance between
| June 15, 2021 | education
From a point located at a distance of 6 cm from the plane, two inclined ones are drawn. Find the distance between the bases of the inclined, if the angle between the inclined and its projection is 30 degrees, and between the projections – 120 degrees.
In a right-angled triangle AOB, we define the length of the leg OA through the known leg and angle. tg30 = BO / AO.
AO = BО / tg30 = 6 / (1 / √3) = 6 * √3 cm.
Similarly, in a triangle BОС СО = 6 * √3 cm.
In the triangle AOB, by the cosine theorem, we determine the length of the segment AC.
AC ^ 2 = AO ^ 2 + CO ^ 2 – 2 * AO * CO * Cos120 = 108 + 108 – 2 * 6 * √3 * 6 * √3 * (-1 / 2) = 216 + 108 = 324.
AC = 18 cm.
Answer: The speaker distance is 18 cm.
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.
