Angles less than 90 degrees are called acute angles. When the time is 11 o'clock, for instance, the angle formed by the hour and minute hands is acute. Acute angles are defined as 30°, 40°, 57°, and so on.
What is an Acute Angle?
An angle is formed when two rays meet at a vertex. Acute angles are those that are smaller than 90 degrees in length. In the diagram below, the angle formed by 'Ray 1' and 'Ray 2' is acute. When you divide a right angle in half, you get two acute angles.
Also Check: Types of Angles
Acute Angle Definition
Acute angles are these which are less than 90 degrees, or between 0 and 90 degrees. Some examples include 60 degrees, 30 degrees, 45 degrees, and so on. The interior angles of an acute triangle are all less than 90 degrees. An equilateral triangle is an acute triangle because the internal angles measure 60 degrees.
Acute Angle Degree
An acute angle is one which is less than 90 degrees, or less than a straight angle, as we taught in the previous section. Acute angle degrees include 63°, 31°, 44°, 68°, 83°, and 85°. The acute angle degree ranges from 0 to less than 90 degrees as a result. Below are some diagrammatic representations of acute angles.
Real-Life Examples of Acute Angles
Acute angles are defined as those that are larger than 0° but less than 90° in geometry. As a result, acute angles include 45 degrees, 5 degrees, 28 degrees, 49 degrees, and 89 degrees.
Here are some real-life examples of acute angles.
- Watermelon slice that has been cut into little pieces.
- Some examples of the angles formed by a clock's hour and minute hands.
- When the beak of a bird is fully open.
- When the mouth of a crocodile is open.
Acute Angle Triangle Properties
In an acute triangle, all of the angles are less than 90 degrees. When all three angles of a triangle are 60 degrees, the triangle is termed an equilateral triangle. There are three forms of acute triangles: acute scalene, acute isosceles, and equilateral triangles. The acute triangle is one of several different triangle types. In the triangle below, all of the interior angles are less than 90 degrees. As a result, the shape is referred to as an acute triangle.
Acute Angle Formula
We have an acute angle triangle formula, often known as the triangle inequality theorem for acute angle triangles, similar to the Pythagoras theorem for right triangles. The total of the squares of the two sides of a triangle is bigger than the square of the largest side, according to this rule. If the sides of ABC measure a,b,c, with c being the biggest, then a2 + b2 > c2. In other words, an acute triangle is defined as a2 + b2 > c2.
Frequently Asked Questions
Here are the seven types of angles commonly studied in geometry:
- Acute Angle: Measures less than 90 degrees.
- Right Angle: Measures exactly 90 degrees.
- Obtuse Angle: Measures more than 90 degrees but less than 180 degrees.
- Straight Angle: Measures exactly 180 degrees.
- Reflex Angle: Measures more than 180 degrees but less than 360 degrees.
- Full Angle: Measures exactly 360 degrees.
- Supplementary Angles: Two angles whose measures add up to 180 degrees.
Yes, an acute angle can be 45 degrees. An acute angle is any angle that measures less than 90 degrees, so 45 degrees qualifies as an acute angle. It is one of the common measures for acute angles in geometry.
Three examples of acute angles are:
- 30 Degrees: An angle that measures 30 degrees, which is less than 90 degrees.
- 45 Degrees: An angle that measures 45 degrees, often used in geometric shapes and trigonometric functions.
- 60 Degrees: An angle that measures 60 degrees, commonly seen in equilateral triangles where all angles are acute.
The main difference between acute and obtuse angles is their measures. An acute angle is always less than 90 degrees, while an obtuse angle is greater than 90 degrees but less than 180 degrees. For instance, a 60-degree angle is acute, whereas a 120-degree angle is obtuse.
No, an angle cannot be both acute and obtuse. An acute angle measures less than 90 degrees, while an obtuse angle measures more than 90 degrees. Each angle fits into only one of these categories based on its measure.