# In triangle ABC, the angle at the vertex C is 90 degrees and the outer angle at the vertex A is 150 degrees.

In triangle ABC, the angle at the vertex C is 90 degrees and the outer angle at the vertex A is 150 degrees. The smaller side of the triangle is 12.5. Find the length of the diameter of the circle described around this triangle.

The angle BAC is adjacent to the outer corners BAD, then the angle BAC = 180 – BAD = 180 – 150 = 30.

The BC leg lies against an angle of 30, then AB = 2 * BC = 2 * 12.5 = 25 cm.

Since triangle ABC is rectangular, the diameter of the circumscribed circle around it coincides with the hypotenuse of the triangle.

Then D = AB = 25 cm.

Answer: The diameter of the circumscribed circle is 25 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.