The answer to the question “What is the greatest number of acute angles a triangle can contain?” is three. A triangle is a two-dimensional shape defined by three straight sides, with each side connecting two angles. The angles inside a triangle can range from 0° to 180°, but the sum of the angles must add up to 180°.

When it comes to the angles of a triangle, there are three types: acute, obtuse, and right. An acute angle is defined as an angle that is less than 90° and is considered the sharpest angle that can be made, while an obtuse angle is greater than 90° and is considered the widest angle that can be made. A right angle is an angle of exactly 90° and forms a perfect square corner.

For a triangle to contain three acute angles, all of the angles must be less than 90°. This means that the sum of the angles must be equal to 180°, but each individual angle must be less than 90°. This type of triangle is known as an acute triangle, and it is the triangle with the highest number of acute angles that can exist.

An acute triangle has a number of interesting properties. For example, it has the smallest possible perimeter and area of all triangles, and the sides of an acute triangle always have a ratio of 1:1:1. It is also the only type of triangle in which the internal angles are all acute angles, making it the only triangle with three acute angles.

In summary, the greatest number of acute angles a triangle can contain is three. An acute triangle contains three angles less than 90°, making it the only triangle with three acute angles. It also has a number of interesting properties, including the smallest possible perimeter and area of all triangles, and sides with a ratio of 1:1:1.