What is a 45 degree angle?

A 45-degree angle has several key properties:

• It's an acute angle: Acute angles measure less than 90 degrees.

• It's half a right angle: A right angle measures 90 degrees, so a 45-degree angle is exactly half of that.

• In an isosceles right triangle: A 45-degree angle is always found in an isosceles right triangle. This is a right triangle (containing one 90-degree angle) where the two legs (the sides that form the right angle) are of equal length. The other two angles in this triangle are both 45 degrees.

• Trigonometric ratios: For a 45-degree angle (often denoted as π/4 radians):

  • sin(45°) = cos(45°) = √2 / 2 ≈ 0.707
  • tan(45°) = 1

• Geometric constructions: A 45-degree angle is easily constructed using a compass and straightedge by bisecting a right angle.

• Applications: 45-degree angles appear frequently in architecture, engineering, and design, often for symmetry and structural reasons. They're also common in many geometric problems and calculations.