Acute Angles and its Real-life Examples

An angle that is smaller than the right angle is known as the acute angle. This means that acute angles are less than 90-degrees. Did you know, a pair of tweezers, a pair of open scissors can create an acute angle? For example, 45-degrees, 60-degrees, 30-degrees, 15-degrees are all acute angles. There are polygons like triangle, trapezoid, and parallelogram that consist of at least one acute angle. This topic can be easily understood and grasped. In this article, we will try to learn about the properties of an acute angle, real-life examples, and some examples related to it. 

Properties of Acute Angle

1. All equilateral triangles are considered acute triangles. An equilateral triangle is a triangle having three sides of the same length and three angles of the equal measure that is 60 degrees. 

2. Acute triangles can be of various types such as the isosceles, scalene, and equilateral triangle. 

3. The longest side of an acute triangle is the opposite side of it. 

4. The main property of acute angle is that it always lies between the measurement of 0 degrees to 90 degrees. 

Some Real-life Examples of Acute Angle

1. The angle made by the letter v is also an acute angle. 

2. Have you ever eaten a pizza slice? If we cut a pizza slice into four pieces, each piece will create an acute angle. 

3. If we cut a watermelon into small pieces, each piece creates an acute angle. 

4. You might have seen some road signs, namely, one way and no right turn. These arrows show an acute angle. 

5. When the beak of a bird is open or the mouth of a crocodile, all form an acute angle, less than 90 degrees. 

Acute Angle vs Obtuse Angle

1. The measure of an angle that is less than 90 degrees is known as acute angle whereas an angle that is greater than 90 degrees but smaller than 180 degrees is known as an obtuse angle. 

2. A triangle can have more than one acute angle whereas a triangle cannot have more than one obtuse angle. 

3. An acute angle always measures smaller than a right angle whereas an obtuse angle always measures higher than a right angle. 

Formula of Acute Angle

In an acute triangle, the following statement holds true on the length of the sides 

1. a.a + b.b > c.c

2. b.b + c.c > a.a

3. c.c + a.a > b.b

Let us see some examples related to the formula of an acute angle to understand the concept more clearly.

Q. Angle A measures x degrees. Is A acute if x = 12°? If x = 75°? If x = 90°? If x = 235°?


When x = 12°:

12 < 90

Yes, ∠A is an acute angle.

When x = 75°:

75 < 90

Yes, ∠A is acute angle.

When x= 90°

90 < 90 (not true)

Alternatively, 90 = 90

So, ∠A is not acute if x = 90°.

When x = 235°:

235 < 90 (not true since 235 > 90)

So, ∠A is not acute if x = 235°.

Q. The angles of a triangle measure 35°, 45°, and 90°. Is it an acute triangle?


We know very well that all the sides of an acute triangle measure less than 90°. From the given question, we can see that the two angles that are 35° and 45° measure less than 90°. However, the third angle is 90°. Thus, the triangle is not an acute triangle.

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