Acute Inscribed Right Triangle:
An acute inscribed right triangle is a special type of triangle that is formed inside a circle where one of the angles is a right angle and the other two angles are acute angles.

Acute Angle:
- An acute angle is an angle that measures less than 90 degrees. In a triangle, all three angles must add up to 180 degrees, so in an acute inscribed right triangle, one angle is 90 degrees and the other two angles are less than 90 degrees.

Inscribed Triangle:
- An inscribed triangle is a triangle that is contained within a circle where each vertex of the triangle lies on the circumference of the circle.

Properties of an Acute Inscribed Right Triangle:
- In an acute inscribed right triangle, the hypotenuse (the side opposite the right angle) is the diameter of the circle.
- The acute angles of the triangle are formed by connecting the endpoints of the diameter to any point on the circumference of the circle.
- The acute inscribed right triangle is unique in that it is the only right triangle that can be inscribed in a circle.

Applications:
- The concept of acute inscribed right triangles is commonly used in geometry and trigonometry to solve problems related to circles and right triangles.
- Understanding the properties of these triangles can help in calculating various geometric measurements and relationships within circles.