Rectangle ABCD and right triangle DCK lie in different planes. Vertex K is projected to point B
May 27, 2021 | education
| Rectangle ABCD and right triangle DCK lie in different planes. Vertex K is projected to point B. BK = 4cm, AB = 4√2, AD = 4. Calculate the distance between lines AB and KC.
Since ABCD is a rectangle, BC = AD = 4 cm.
Point K is projected to point B, then BK is perpendicular to square ABCD, and triangle BSC is rectangular and isosceles, BC = BK = 4 cm.
Let us define the length of the hypotenuse СK.
CK ^ 2 = BK ^ 2 + BC ^ 2 = 16 + 16 = 32.
СK = 4 * √2 cm.
The plane BCK is perpendicular to the plane of the square, then the height BH of the triangle BCK is the desired distance.
KH = CH = KC / 2 = 4 * √2 / 2 = 2 * √2 cm.
Then BH ^ 2 = BK ^ 2 – KH ^ 2 = 16 – 8 = 8.
BH = 2 * √2 cm.
Answer: The distance between the lines is 2 * √2 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.