# Explore More About the Right Angle in Geometry

## Right Angle

The right angle can be understood as a situation when the two straight lines meet each other or intersect each other at an angle of 90 degrees. In brief words, the right angle is the angle made by the two straight lines, when they are upright to each other. 90 degrees can also be exemplified by π/2.

### Right – Angled Triangle

In a right-angled triangle, there are three sides. Those three sides are named, a base, a hypotenuse, and a perpendicular.

For a right-angled triangle, there is a theorem that is known as the Pythagorean theorem.

The theorem is,

h*h = b*b + p*p

### Examples

We will be discussing the examples of the right angle for a better understanding of the concepts of the right angle.

Example 1: There is a right-angled triangle named QPR. The base of the angle is QP. The length of the b is 4 cm. The l hypotenuse of this triangle is RQ. The length of the triangle is 2 cm. One has to find the length of the perpendicular of this triangle QPR.

Solution:

In a given triangle QPR,

QP = 4 cm

RQ = 2 cm

RP = we have to find

From the above mentioned Pythagorean formula, we know that,

h*h= b*b + p*p

Putting the values in the formula,

We will get

2*2 = 4*4 + p*p

The final solution to this will be the perpendicular of this right-angled triangle QPR.

Example 2: There is a right-angled triangle named, TPI. The base of the triangle TPI is PI. The length of the b is 4 cm. The perpendicular of the triangle is TP. The length of the p is 5 cm. One has to find the hypotenuse of this triangle TPI.

Solution:

In a given triangle TPI,

PI =  4 cm

TP = 5 cm

TI = we have to find

From the above-mentioned formula, we get that,

4*4+5*5 = h*h

The solution to this will be the hypotenuse of this triangle.

### Examples of Right Angles in Real Life

A few examples of right Angles from our day-to-day lives will help a lot in understanding this more clearly. Some of those examples are:

• Corners of a television.
• Corners of a door.
• Corners of a room.
• Corners of a notebook or a textbook.

### Examples of Geometrical Figures Having Right Angles

Now, we will be mentioning some of the geometrical figures that have right angles in them:

• In a Square –

In a square, all the angles are 90 degrees. Presume that there is a square named, ABCD. Then, all the angles of this particular square, angle A, angle B, angle C, and angle D are 90 degrees.

• In a Rectangle –

In a rectangle, all the angles are 90 degrees. Presume that there is a rectangle named LMNB. Then, all the angles of this particular rectangle, angle L, angle M, angle N, and angle B are 90 degrees.

• In a right-angled Triangle-

In a right-angled triangle, one of the three angles is 90 degrees. Presume that there is a triangle named DFG. In a DFG triangle, the angle F will be 90 degrees.

### Obtuse Angle

The obtuse angle is an angle having measurements of more than 90 degrees. Any angle that is more than 90 degrees is understood to be an obtuse angle.

### Here are a few examples of an obtuse angle:

• 143 degrees
• 149 degrees
• 178 degrees
• 177 degrees
• 168 degrees

Note: An obtuse angle should not be more than 180 degrees.

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