Acute Angle
An acute angle is an angle that measures less than 90°. For example, when the time is 11 o'clock, the angle formed between the hour hand and the minute hand is an acute angle. In other words, 30°, 40°, 57°, and so on are all acute angles.
| 1. | What is an Acute Angle? |
| 2. | Real-Life Examples of Acute Angles |
| 3. | Acute Angle Triangle Properties |
| 4. | FAQs on Acute Angle |
What is an Acute Angle?
An angle is formed when two rays meet at a vertex. When this angle measures less than 90°, it is termed an acute angle. In the figure shown below, the angle formed between 'Ray 1' and 'Ray 2' is an acute angle.
Acute Angle Definition
An acute angle is defined as an angle that measures between 0° to 90°. Some of the examples of acute angles are 60°, 30°, 45 degrees, etc.
Acute Angle Degree
In the section given above, we learnt that an angle that measures less than 90 degrees, i.e., less than a right angle is an acute angle. The examples of acute angle degrees are 63°, 31°, 44°, 68°, 83°, 85°. Hence, the acute angle degree lies within the ranges from 0° to less than 90°. Here are a few diagrammatic representations of acute angles.
Real-Life Examples of Acute Angles
We know that angles measuring greater than 0° and less than 90° are called acute angles in geometry. Therefore, 45°, 5°, 28°, 49°, and 89° are all examples of acute angles.
Here are some real-life examples of acute angles.
- The beak of a bird when it is open.
- A pair of open scissors.
- The angle that is formed when a crocodile's mouth is open.
Acute Angle Triangle Properties
An acute triangle has all its angles less than 90°. When all three angles of a triangle are 60°, it forms a special triangle called an equilateral triangle. Acute triangles can be classified as acute scalene triangles, acute isosceles triangles, and equilateral triangles. There are many types of triangles and the acute triangle is one of them. The triangle shown below has all of its interior angles less than 90°. Therefore, it is called an acute triangle.
Acute Angle Formula
Just like the Pythagoras theorem for right triangles, we have an acute angle triangle formula which is often known as the triangle inequality theorem for acute angle triangles. It states that the sum of the squares of the two sides of a triangle is greater than the square of the largest side. In Δ ABC, if the sides measure a,b,c such that 'c' is the largest side, then, a2 + b2 > c2. In other words, in a triangle, if a2 + b2 > c2, the triangle is an acute triangle.
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Acute Angle Examples
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Example 1: Choose the angles which can be classified as acute angles.
Solution:
Option a) 40° is less than 90°. Therefore, it is an acute angle.
Option b) 117° is more than 90°. Therefore, it is not an acute angle, it is an obtuse angle.
Option c) 121° is more than 90°. Therefore, it is not an acute angle, it is an obtuse angle.
Option d) 60° is less than 90°. Therefore, it is an acute angle.
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Example 2: Observe the clocks shown below and identify the times at which the hands form an acute angle.
Solution:
We can observe that at 10 o'clock and 11 o'clock, the hour hand and the minute hand form an acute angle.
Therefore, an acute angle is formed by the clocks at 10 o'clock and 11 o'clock.
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Example 3: Is the following triangle acute?
Solution:
All the 3 angles inside an acute triangle should measure less than 90°. From the figure, we can see that two angles measure 45° each and ∠Y is 90°. Hence, this is not an acute triangle, it is a right-angled triangle.
FAQs on Acute Angle
What is an Acute Angle?
An acute angle is an angle that measures less than 90°. It can be measured using a protractor. For example, 35°, 60°, 72°, and so on are all acute angles.
What are Some Examples of Acute Angles?
Acute angles are angles that measure less than 90°. Therefore, 10°, 30°, 45°, and 70° are some examples of acute angles.
How to Find the Measure of an Acute Angle?
Acute angles can be measured with the help of a protractor. To measure an acute angle, place the bottom line of the protractor on the baseline and place the center of the protractor on the vertex where the two lines meet. Now, consider the bottom scale of the protractor and measure the angle.
What is an Acute Angle Triangle?
An acute angle triangle is one in which all the internal angles are less than 90°. For example, an equilateral triangle has all of its internal angles equal to 60°. So, it can be referred to as an acute angle triangle.
What are the Properties of an Acute Angle Triangle?
There are a few important properties that help us identify an acute triangle easily.
- The three interior angles of an acute angle triangle sum up to 180°.
- A triangle cannot be an acute-angled triangle and a right-angled triangle at the same time.
- A triangle cannot be an obtuse-angled triangle and an acute-angled triangle at the same time.
- All three angles of an acute angle triangle are always less than 90°
What are the Characteristics of an Acute Angle?
The main characteristic of an acute angle is that it lies between 0° to 90°. The shape of an acute angle looks like the shape of an open pair of scissors or when the hour hand and the minute hand of the clock show 10 o'clock or 11 o'clock.
What is the Least Number of Acute Angles a Right Triangle Has?
A right triangle must have at least two acute angles in it. One angle should measure 90 degrees and the other two always lie between 0° to 90°.
What Does an Acute Angle Look Like?
An acute angle lies between 0° and 90°. A pair of open scissors look like an acute angle. The hands of the clock form an acute angle at 11' o clock.
Is a Right Angle Triangle an Acute Angle Triangle?
No, a right-angled triangle is not an acute-angle triangle. In a right triangle, one interior angle is 90° and the other two angles are 45° each. For a triangle to be an acute angle triangle, all the internal angles need to be less than 90°. So we can say that a right-angled triangle is not an acute triangle.
What is the Difference Between Acute and Obtuse Angles?
Obtuse angles measure more than 90° (but less than 180°), and acute angles measure less than 90°. For example, 110° is an obtuse angle and 50° is an acute angle.
What is the Meaning of Acute Angle?
An acute angle is an angle that measures less than 90°. In other words, an acute angle lies between 0° and 90°. For example, 20°, 55°, 45°, and 67° are called acute angles.