A triangle with two sides equal to 24 cm and 12√3 cm. inscribed in a circle with a radius of 12 cm. Determine the angles of the triangle.

univerkov | February 23, 2021 | education

Let us apply the sine theorem for a triangle inscribed in a circle.

AC / SinABC = 2 * R.

SinABC = AC / 2 * R = 12 * √3 / 2 * 12 = √3 / 2.

Angle ABC = arcsin (√3 / 2) = 60.

AB / SinACB = 2 * R.

SinACB = AB / 2 * R = 24/2 * 12 = 1.

Angle ACB = arcsin (1) = 90.

Then the angle BAC = (180 – 90 – 60) = 30.

Answer: The angles of the inscribed triangle are 30, 60, 90.

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.