Acute Angle – Definition, Diagrams, Examples, Properties, and Formula

Whenever you see an angle that measures less than 90 degrees then affirm it as the acute angle. An acute angle is formed by the two arms of the clock when the time is 11 o’clock. A few examples are 30 degrees, 40 degrees, and 60 degrees. Do you know how an angle is formed? An angle is formed when two rays meet at a point which is known as the vertex point. When this angle is measured and the result comes as less than 90 degrees, then this is known as the acute angle.

Drawing Two Acute Angle in A Diagram of Two Rays

Follows the following steps which will help us to identify acute angle in a two-ray diagram. The steps are as follows:

• Suppose, there are two rays – Ray 1 and Ray 2
• When these two rays meet at a vertex an angle is formed
• This angle is measured and the result comes as 90 degrees
• Now the 90-degree angle is cut from the central point
• After this division, two angles are formed which measures less than 90 degrees.
• Here you have two acute angles measuring less than 90 degrees.

What is the Different Measurement of An Acute Angle?

As studied, we know what is an Acute Angle, now we will check some angles which are actually Acute Angle. As explained, angles measure less than 90 degrees. Therefore, the angles which are less than 90 degrees will be – 63°, 31°, 44°, 68°, 83°, 85°.

Thus, we see that the acute angle degrees will range from 0 to 90 degrees. Thus, this can be more than 0 degrees but less than 90 degrees.

Examples of Acute Angles

A few examples of acute angles from real life are as follows:

• Slice of melon when cut into small divisions.
• At times when the angles which are formed by the clock also take the measurement of 90 degrees.
• The curved beak of the crow or any other bird.
• The angle is formed when the alligator opens its mouth to catch its prey.

What Will Be the Properties of An Acute Angle?

The properties of the acute angle are:

1. The acute angle has angles that measure less than 90 degrees.
2. Acute angles can form Triangles, which will measure less than 90 degrees.
3. This will also form Acute Scalene Triangles, Acute Isosceles Triangle, and Equilateral Triangle.

How would you Derive the Acute Angle Formula?

We know the Pythagoras Theorem formula which is curated for the right-angled triangles, now for the acute angle triangle, we have the formula which is popularly known as the triangle of inequality formula which is for the acute angle triangles.

The formula states that the sum of the squares of any two sides of a triangle being greater than the square of the largest side, then it shall be proved that it is an acute-angled triangle.

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