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Right Angle

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A Right Angle is an angle whose measure in degrees is 90 degrees and its measure in radians is π/2 radian. It is one of the most basic angles in geometry and has various applications. It is used to define various shapes, structures, and figures in 2-D and 3-D space. Two lines that are perpendicular to each other always form the right angles. We can see the right angles at various figures such as we see right angles at the corners of squares and rectangles, i.e. the sides meeting at the corners of the rectangle forms the right angles.

In this article, we will learn about the right angle definition, the right angle shape along with the right angle triangle, and area of right angle triangle.

What is a Right Angle?

An angle that has a measure equal to 90 degrees is called a Right Angle. It is formed when two rays meet each other perpendicularly. The angle between two perpendicular lines is called the Right Angle. In radian, right angle measures π/2 radian.

Right Angle Definition

A right angle in geometry is an angle that measures exactly 90 degrees and it is formed by intersecting two lines or line segments in such a way that the angle between them on either side is 90 degrees. It is denoted by the symbol (L). We observe right angles at the corner of the screen of Computers, television, etc.

Right Angle Degree

The measure of a right angle triangle in degrees is 90 degrees which can also be represented as, 90°, the figure to two lines OA and OB showing line the right angle is added below,

Right Angle

Right Angle Shapes

The right angle shape is one of the most common shapes of geometry and can be represented by “L”. We see right angles in our daily life regularly, the angle between minutes hand and hour hand at 3:00 pm, 6:00 pm, etc is a right angle. 

The various other real-life examples of the right angle are,

Right Angle Shapes

Right Angle Examples in Real Life

Various examples of right angles that we observed in our real life are,

  • The edges of the screen of our TV, laptops and other screens form the right angle.
  • The corners of the table and the book form the right angle.
  • The set square in the geometry box is an example of a right angle.
  • Various sweets are shaped at right angles.

Right Angle Calculator

We can calculate the right angle using various devices they are called right-angle calculators. Some examples of right-angle calculators are a pair of set squares, a compass, a protractor, etc. All these devices can easily measure the right angle, as for measuring the right angle using set squares we place the set square above the angle that we have to measure and if the set square matches the angle completely then it is a right angle.

Similarly placing the protector above the angle tells us whether the angle is a right angle or not. While using a pair of set squares or the protector we must make sure that the baseline of the angle matches the baseline of this equipment else our reading may set distorted. Various equipment that is used to measure the right angles are described in the image added below,

Right Angle Calculator

Right Angle Triangle 

A Triangle with one of its angles is a right angle i.e. 90° is known as the Right Angle Triangle or a Right Triangle. The side opposite to the right angle is the hypotenuse. A right-angle triangle can never be an equilateral triangle because one of its angles is always 90 degrees. In a right-angled isosceles triangle, the other two angles measure 45 degrees each.

Right Angle Formula

The formula of the Right-angled triangle is explained by Pythagoras Formula. The formula states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagoras Formula is given below,

(H)2 = (B)2 + (P)2

where,

  • H is the Hypotenuse of the Right Angle Triangle
  • B is the Base of the Right Angle Triangle
  • P is the Perpendicular of the Right Angle Triangle

The Image added below shows a right-angle triangle, in which PR is the hypotenuse, PQ is the perpendicular and QR is the base of the right angle triangle.

Right Triangle

The right angle formula for the above triangle is,

PR2 = PQ2 + RQ2

Right Angled Triangle Perimeter

The perimeter of a right triangle is the sum of all the sides. For example, if a, b, and c are the sides of a right triangle, then the perimeter is (a + b + c). Now that this is a right triangle, we can say that its perimeter is equal to the sum of the lengths of the two sides and the length of the hypotenuse. The formula to find the perimeter of a triangle is,

Perimeter of Right Triangle = a + b + c

Right Angled Triangle Area

The area of ​​a right triangle gives the spread or space the triangle occupies. It is equal to half the product of the base times the height of the triangle. Because it is a two-dimensional quantity, it is expressed in square units. The only two sides needed to find the area of ​​a right triangle is the base and the height. Using the definition of a right triangle, the area of ​​a right triangle is given as,

Area of ​​Right Triangle = (1/2 × base × height) = (1/2 × Base × Perpendicular)

Related Resources,

Right Angle Isosceles Triangle

An isosceles triangle is a triangle in which two sides of the triangle are equal. For a right-angled isosceles triangle, we have an isosceles triangle that has a right angle. Now if one angle of the isosceles right-angle triangle is 90 degrees and the other two angles are equal then by following the angle sum property of the triangles we can calculate the other two angles of the triangle.

 Let the other two equal angles be “a”, now

a + a + 90 = 180

2a = 180 – 90 = 90

a = 90/2

a = 45

Thus the measure of the two equal angles of the isosceles right angle triangle is 45 degrees.

Right Angle Triangle Properties

Various properties of the right-angle triangle are,

  • There is no obtuse angle in the Right Angle Triangle
  • A right triangle has only one right angle, i.e. an angle measuring 90 degrees.
  • The longest side of the right-angle triangle is called the hypotenuse.
  • The area of the right-angle triangle is, A = 1/2 × P × B

Also, Read

Right Angle Examples

Example 1: In a Right Angle Triangle, What is the value of hypotenuse if the perpendicular is 4 cm and the base is 5 cm?

Solution:

Given, 

  • Perpendicular = 4 cm
  • Base = 5 cm

By using Pythagoras Formula ,

(H)2 = (B)2 + (P)2 

Where , 

  • H = Hypotenuse
  • B = Base and 
  • P = Perpendicular

(H)2 = (5)2 + (4)2

(H)2 = 25 + 16

(H)2 = 41

H = √41 cm

Thus the hypotenuse of the right angle triangle are √41 cm

Example 2: In a Right Angle Triangle, What is the value of Perpendicular if the hypotenuse is 5 cm and the base is 4 cm?

Solution: 

Given, Hypotenuse = 5 cm and Base = 4 cm.

By using Pythagoras Formula ,

(H)2 = (B)2 + (P)2 

Where , H = Hypotenuse , B = Base and P = Perpendicular

(5)2 = (4)2 + (P)2

25 = 16 + (P)2

(P)2 = 9

P = 3 cm

Example 3: What is the Perimeter of the right Angled triangle, if the Base is 10 m, the Perpendicular is 8 m and the Hypotenuse is 13 m.

Solution:

Given, 

  • Base = 10 m
  • Perpendicular = 8 m 
  • Hypotenuse = 13 m

Using the Perimeter formula of Right Angled triangle,

P = 10 m + 8 m + 13 m 

P = 31 m

Thus, the perimeter of the given right angle is 31 m.

Example 4: What is the Area of the right Angled triangle, if the Base is 10 m, the Perpendicular is 8 m and the Hypotenuse is 18 m. 

Solution:

Given, 

  • Base = 10 m
  • Perpendicular = 8 m 
  • Hypotenuse = 18 m

Using Area formula of Right Angled triangle,

A = 1/2 × Base × Height

A = 1/2 × 10 m × 8 m

A = 80 m / 2

A = 40 m2

Thus, the area of the right angle triangle is 40 m2.

FAQs on Right Angle

1. What is a Right Angle in Math?

A right angle in the math is an angle that has a measure of 90 degrees. It is the angle between two perpendicular lines and the measure of altitude of any figure is right angle.

2. How many degrees are in a Right Angle?

The right angle is measured in degrees and its measure in degree is 90 degrees 

3. How to measure a Right Angle?

A right angle can be measured using a compass and set squares, it is the angle between two perpendicular lines. 

4. What are Examples of a Right Angle?

There are various examples which resembles right angle triangle in our daily life some of them are,

  • The corners of our screen, tables, blackboard,etc are all at right angles.
  • various objects, such as set squares, some sweets, etc are in shape of right angles.

5. What is a Right Angled Triangle?

A right triangle is a type of triangle that has one of its angles measuring exactly 90 degrees (90°). This special angle is called a “right angle.” The other two angles in a right triangle are acute angles, meaning they are smaller than 90 degrees.

6. What is the Formula of Right-Angle Triangle?

The right triangle formula is, suppose we have a right angle triangle, with sides, a, b and c. then the right angle triangle formula is,

a2 + b2 = c2

where,

  • a and b are the perpendicular and the base of the right angle triangle
  • c is the hypotenuse of the right angle triangle

This formula is also called the Pythagoras Theorem.

7. How many Acute Angles are in a Right Triangle?

A right angled triangle follows the angle sum property of triangle and hence, if one angle of the triangle is 90° its other two angles must add up to 90°, that implies the other two individual angles are individually less than 90° and hence the other two angles in the right angle are acute angles. Thus a right triangle has 2 acute angles.

8. What is the Area of a Right Angled Triangle?

The area of a right triangle can be calculated using the following formula:

Area = (1/2) × base × height



Last Updated : 10 Jan, 2024
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