The point is located at a distance of 10 cm from all vertices of an equilateral triangle with a side of 6√3 cm

| March 26, 2021 | education

The point is located at a distance of 10 cm from all vertices of an equilateral triangle with a side of 6√3 cm. Find the distance from this point to the plane of the triangle.

Based on the condition, the distance from a point to the plane of the triangle is the height dropped by the triangle. Based on the fact that we have an equilateral triangle, then this height will drop to the center of the circumscribed circle. Since the height drops at a right angle, we get a right-angled triangle with a hypotenuse of 10 cm and a leg, which is the radius of the circumscribed circle. We calculate the length of the radius using the formula:
r = √3 / 3 * a = √3 / 3 * 6√3 = 6 * 3/3 = 6 cm.
Knowing that the leg is 6 cm, and the hypotenuse is 10 cm, we calculate the second leg, that is, the height according to the Pythagorean theorem.
b ^ 2 = 10 * 10-6 * 6 = 100-36 = 64
b = √64 = 8 cm.
Answer: 8 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.