An angle that measures less than 90° is called an acute angle. 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.||Examples of Acute Angles|
|3.||Acute Triangle Properties|
|4.||Solved Examples on Acute Angle|
|5.||Practice Questions on Acute Angle|
|6.||Frequently Asked Questions (FAQs)|
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 as an acute angle. In the figure shown below, the angle formed between 'Ray 1' and 'Ray 2' is an acute angle. Also, when a right angle is divided into two it forms two acute angles.
Here are a few more examples of acute angles.
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°, 89° are all examples of acute angles.
Here are some real-life examples of acute angles.
- A slice of watermelon, when cut in small portions as shown below.
- Some instances of the angles formed between the hour's hand and the minute's hand of a clock.
- The beak of a bird when it is open.
- The angle formed when a crocodile's mouth is open.
Acute 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 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.
Triangle Inequality Theorem for an Acute Triangle
Just like the Pythagoras theorem for right triangles, we have a triangle inequality theorem for acute 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.
Topics Related to Acute Angle
Check out some interesting topics related to an acute angle.
Solved Examples on Acute Angle
Example 1: Choose the angles which can be classified as acute angles.
Option a) and option d) measure less than 90°. Hence, they are acute angles.
Example 2: Observe the clocks shown below and identify the times at which the hands form an acute angle.
We can observe that at 10 o'clock and 11 o'clock, the angle formed between the hour hand and the minute hand is an acute angle. Therefore, an acute angle is formed by the clocks that show 10 o'clock and 11 o'clock.
Example 3: Is the following triangle acute?
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.
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°, 70° are some examples of acute angles.
How do you 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 angles lines meet. Now, consider the bottom scale of the protractor and measure the angle.
What is an Acute Triangle?
An acute triangle is one in which all the internal angles of a triangle 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 triangle.
Is a Right Triangle an Acute Triangle?
No, a right triangle is not an acute triangle. A right triangle has one of its interior angles to be 90° and the other two angles as 45° each. For a triangle to be an acute 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 Obtuse and Acute 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.