Acute Angle-Definition, Properties, And Formula

An acute angle is an angle that measures less than 90°. For example, if the time is 11 o’clock, the angle between the hour hand and the minute hand is an acute angle. So, 30°, 40°, 57°, and so on are all acute angles.

What is an Angle?

Two line segments or rays meet at a common endpoint to form an angle. The endpoint where they meet is called the vertex of the angle. The lines that intersect to form an angle are called the angle’s arms. An angle is represented by the symbol ‘∠’ and is measured in degrees (o) with the help of a protractor.

What is an acute Angle?

An angle measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is 90 degrees). For example, angles such as ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, and ∠85o are all acute angles. The angle formed between ‘Ray 1’ and ‘Ray 2’ in the figure below is an acute angle. Additionally, when a right angle is divided into two, it forms two acute angles.

Acute Angle Degree

An acute angle is an angle whose degree measures less than 90 degrees, or less than a right angle. Examples of acute angle degrees are 12°, 35°, 48°, 65°, 80°, and 89°. Hence, the acute angle degree ranges from 0 degrees and less than 90 degrees.

Acute Angle Formula

If you have an acute triangle, the following statement will be true for the length of the sides:

a² + b² > c²

b² + c² > a²

c² + a² > b²

Where a, b, and c are the lengths of each side of the triangle.

Acute Angle Images

The below figure shows images of acute angles measuring 40degrees.

Real-Life Example of Acute Angles

• The angle made in the letter V is an acute angle.
• The beak of a bird is open when the angle is formed by the crocodile’s mouth.
• The hour and minute hands of a wall clock form acute angles at several hours of the day – for example, at 1 o’clock.
•  Road signs such as “One Way” and “No Left Turn” arrows also form acute angles.
• The turn signal indicator and the speedometer on the dashboard both form acute angles inside the vehicle.

Acute Triangle

If all the internal angles of a triangle are less than 90 degrees, then the triangle is called acute

Properties of Acute Triangle

• All equilateral triangles are acute triangles.

An equilateral triangle has three sides of the same length and three angles of equal measure, i.e. 60°

• The longest side of an acute triangle is opposite the highest angle.
• Acute triangles can be isosceles, equilateral, or scalene.

Frequently Asked Question-FAQs