What is a Right Angle? Definition, Formulas, and Triangle

An angle that is 90 degrees is referred to as a right angle. In our daily lives, it is the angle that is most often seen. It may be observed on the screens of mobile phones, the edges of boxes, and the corners of rooms. So what is a right angle? In this essay, let’s talk more about the right angle.

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what is a right angle

What is a Right Angle?

A right angle is defined in geometry and trigonometry as being precisely 90 degrees, or /2 radians, which corresponds to a quarter rotation. A right angle, which has the form of the letter “L,” measures 90 degrees. The neighboring angles are right angles if a ray is positioned so that its terminus is on a line and they are equal. Angulus rectus, which in this context refers to the vertical line perpendicular to a horizontal baseline and signifies “upright,” is the root of the phrase.

Perpendicular lines, which are defined as lines that cross at right angles, and orthogonality, which is the characteristic of producing right angles, are closely connected and significant geometrical notions. Right triangles are identified by the existence of a right angle, making the right angle a fundamental concept in trigonometry.

Where are the Right Angles Present?

We’ve previously covered a few real-world examples of how to determine the appropriate angles. That’s not it, however! We will learn about all the locations where right angles may be found in this part. The following is a list of all the right angle’s mathematical properties:

One of the angles of a right-angled triangle is 90 degrees.
A square and a rectangle both have four equal sides that form right angles with one another, or we might say that all four of their internal angles are 90 degrees.
A square and a rhombus’ diagonals meet at a straight angle.
Your bedroom’s corners, where you study or sleep, are at an angle.
The angles of a cube and cuboid are all 90 degrees. Take a Rubik’s cube, for instance.

Making a Right Angle: What to Do?

what is a right angle

Making two straight lines is the quickest and easiest technique to create a right angle. Create two lines, one vertical and the other horizontal. Make the intersections between them. The right angle will be created between the two lines. Verify that the lines are straight both vertically and horizontally. For this, a scale may be used. However, this approach is not always reliable. Your hand may slip often, producing a skewed line. Let’s discover two techniques for creating the ideal right angle every time.

First Approach: Protractor

Step 1: Grab a scale, then in your notepad, draw a straight horizontal line.
Step 2: Align your protractor above the horizontal line by using it now. Make sure to accomplish this so that the horizontal line you drew and the protractor’s final, lowest line-up.
Step 3: Make a point slightly above the point marked 90 on your protractor when you look at it. This is when the horizontal line turns 90 degrees.
Step 4: Using the scale once again, draw a straight line from the spot you indicated to the horizontal line using a protractor.
Step 5: Congratulations, you created the ideal right angle.

Remember: Before using your measures and protractors, always clean them. They could smear your work with graphite or ink from the last assignment they were employed for.

Second Approach: Compass

Step 1: Write AB on a horizontal line you drew on your notepad.
Step 2: Grab your compass in step two. Put your pencil inside of it, then align the pencil’s tip with the compass’s tip. Measure an angle now.
Step 3: With the compass’s pointer on point “A,” slide the pencil to draw an arc on the line.
Step 4: Label “C” the location where the arc intersects the line “AB.”
Step 5: Next, position the tip at point “C” and draw a second arc over the previous one. I’ll give it a D.
Step 6: Next, draw another arc over the previous one by positioning the tip at point “D.” Add a point “E” to it. Use the point that is directly above the horizontal line to create another arc as well.
Step 7: Cut the arc you created above the horizontal line with the tip at point E. The junction is known as F.
Step 8: Sketch a straight line connecting points F and A.
Step 9: Congratulations, you just drew a right angle.

You are now proficient at drawing the ideal right angle. To create perfect right angles, you may also experiment with squares and set squares. They have a right-angled triangular form instead of being scale-like. We will learn more about right-angle triangles and how to determine their angles in the section that follows.

Right Angle Triangle

We are all aware that a triangle has three different angles inside it, therefore when one of those angles has a value that is precisely equal to 90 degrees, we refer to that particular triangle as a right-angled triangle. The two angles that are not 90 degrees to the right angle are always sharp in a triangle with a right angle. The combined measure of the two sharp angles must always equal ninety degrees. This may be shown by looking at the example down below:

Let’s say that triangle ABC is a right triangle since it has a right angle at the A point. We are aware that according to the angle sum property of a triangle, the sum of the three angles that are included inside a triangle must be equal to 180 degrees.

As a result, A + B + C = 180˚.

90˚ + B + C = 180˚

B + C = 180˚ – 90˚

B + C = 90˚

In addition to being differentiated by factors like side and angle, right-angled triangles may be divided into two categories:

Isosceles Right Triangle: An isosceles right-angled triangle is a kind of triangle that combines the characteristics of a right-angled triangle with those of an isosceles triangle. It is a triangle with two equal sides, and the angle formed by the lines that connect the three points is precisely 90 degrees.
Right Scalene Triangle: This kind of triangle combines the characteristics of a scalene triangle and a right-angled triangle. In this kind of triangle, each side is not the same length, and only one of the angles has a measure of 90 degrees.

Let’s move on to some more vocabulary about triangles with right angles:

Perpendicular: The height of the right angle triangle is referred to as the perpendicular, and it is one of the three sides of the triangle.
Base: The base of the right-angled triangle is the side that the triangle is constructed on, hence this is the base of the triangle.
Hypotenuse: The name given to the side of a right triangle that is the longest overall is called the hypotenuse.

Always forming right angles with one another, the perpendicular and the base of the triangle always meet at 90 degrees. It is impossible for the hypotenuse and the base or the hypotenuse and the perpendicular to ever produce a straight angle. They can only produce angles that are quite sharp.

Pythagoras, a Greek mathematician, is credited with developing the formula for a right triangle because of the unique nature of this kind of triangle. The Pythagorean theorem asserts that the square of the hypotenuse in any right-angled triangle is equivalent to the sum of the squares of the perpendicular and the base in that triangle.

Formula: (Hypotenuse)² = (Perpendicular)² + (Base)².

The following is a list of several instances taken from the real life of a right triangle:

The slide that was built for children to use in the park is an example of a triangle with right angles.
The concept of trigonometry is often considered to be the greatest and most well-known illustration of a triangle with three right angles. Trigonometry is the foundation for a whole area of mathematics, which is an interesting and significant finding in mathematics. In addition, trigonometry is the area of mathematics that teachers and students alike dread the most.

Key Points to Keep in Mind

Two lines are said to be perpendicular to one other when they meet at right angles to one.
A right angle has a degree measurement of 90 degrees and is formed using the base and the hypotenuse.
On construction sites, right angles are most often employed to give enough support in the corners of the building.
They are essential in the construction of long-span bridges as well as culverts.
In real life, right angles are considered to be quite powerful. When subjected to circumstances of intensive use, the angle does not break. This is due to the fact that it receives support from both sides.

Final Words

What is a right angle? The answer has been detailedly mentioned above. Hope that this article on the right angle can give you the most beneficial information to solve math problems. If you are planning to teach your kids about this essential topic, you can make your own collections of right-angle worksheets using our worksheet maker. Good luck!