The lateral side of an isosceles triangle is 4. The angle at the apex opposite to the base is 120 °. Find the diameter of the circle

| November 22, 2020 | education

The lateral side of an isosceles triangle is 4. The angle at the apex opposite to the base is 120 °. Find the diameter of the circle around this triangle. how to solve without sines

The radius (half the diameter) is calculated by the formula R = a ^ 2 * b / 4S, where a is the side of an isosceles triangle, b is the base, S is the area of ​​the triangle. Find the base of this triangle. Draw the height (Bisector and Median) from the top opposite the base. Since the angle against the base is 120 degrees, the angles at the bases are equal to 30 degrees. When constructing the height, we obtain 2 right-angled triangles, in which one angle is 30 degrees => the height of the triangle is 2. By the Pythagorean theorem, we find the base of a right-angled triangle. The base is 2√3. The base of an isosceles triangle is 4√3. Find the area of ​​a triangle S = 4√3 * 2/2 = 4√3. Find the diameter R = 16 * 4√3 / 4 * 4√3 = 4. The radius is 4 and the diameter is 8.



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.