Introduction to Right Angle Triangle
A triangle is referred to as a regular polygon that has three sides. The unique property of a triangle is that the sum of any two sides of the triangle is always greater than the measure of the third side of the triangle. In simpler words, a triangle is just a closed figure of three sides that has a sum of its angles equal to 180degree. Each shape of the triangle is classified based on the angle made by the two adjacent sides of the particular triangle.
Acute angle triangle
Right angle triangle
Obtuse angle triangle
Right Angled Triangle
The right-angled triangle is the geometrical shape and it is considered as the basics of trigonometry. A right-angled triangle has 3 sides:
Base
Hypotenuse
Height
The angle formed between the base and the height of the triangle is always of 90degrees.
Properties of Right - Angled Triangle
All the properties of the right-angled triangle are mentioned below:
One angle of the triangle always measures 90degree.
The hypotenuse is the longest side of the right-angle triangle.
The side that is opposite to the 90degree angle is the hypotenuse.
The Sum of two interior angles of the right-angled triangle is always 90degree.
The sides adjacent to the 90degree/right angle in the triangle are known as the base and perpendicular of the triangle.
When you draw the perpendicular from the right angle of the triangle and join it to the hypotenuse, you will always get three similar kinds of triangles.
Considering the fact, if one angle of the right-angle triangle is 90degree and the other two angles are of 45degree each, then this type of triangle is known as an Isosceles right-angled triangle. In this, the adjacent side to the angle of 90degree must be equal to each other.
If you draw a circle along the three vertices of the triangle, then the radius of the circle drawn will always be equal to half the actual length of the hypotenuse.
The two angles, other than the angle of 90degree in a right-angle triangle, are always acute angles.
The largest side of a right-angled triangle is known as the Hypotenuse.
Steps to Draw a Right-Angled Triangle
To draw a right-angle triangle is quite simple when the required information for the construction of the same is given or known to you.
To construct a right-angle triangle, the measurement of the hypotenuse of the triangle and the measurement of either of the remaining two sides, base and perpendicular, must be given to you. So, let’s proceed in the form of activity.
Question. The length of the hypotenuse of the triangle is 5cm and the length of the other side of the triangle is 3cm. Construct a right-angled triangle according to the given information.
Aim – To Construct a Right-Angled Triangle
Material Required –
Ruler/scale
Compass
Pen or a pencil
Eraser
Sharper
Sheet
Steps of Construction –
First, you have to draw a horizontal line on a sheet with the help of a ruler and a pencil. The line can be of any measurement.
Mark a point C on the horizontal line.
Now, set the width of the compass as 3cm using a scale.
Now, place the pointer of the compass on point C.
Mark one arc on both sides from point C.
Label the points where arcs cross the lines as P and A, respectively.
Now, set the length of the hypotenuse in the compass, as given in the question.
Hence, the compass width is now set as 5cm.
Now place the pointer of the compass on point P.
Now draw an arc above point C by placing the compass on point P.
Now, repeat the previous step from point A.
Now, mark the point where two arcs from point A and Point P cross each other as B.
Join points A and B using a scale
Join points B and C using a scale.
Right Triangle Formula
Pythagoras, the renowned Greek philosopher, derived an important formula for a right triangle. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs, according to the formula. Pythagoras' theorem was named after him. The following is a representation of the right triangle formula: The sum of the squares of the base and height equals the square of the hypotenuse.
We have the following in a right triangle:
\[(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}\]
Pythagorean Triplet: The Pythagorean triplets are the three numbers that fulfill the preceding equation. For example, the Pythagorean triplet (3, 4, 5) is a Pythagorean triplet since \[3^{2} = 9, 4^{2} = 16, and 5^{2} = 25\] and 9 +16 = 25. As a result, \[3^{2} + 4^{2} = 5^{2}\]. The Pythagorean triplet is a set of three integers that meet this requirement.
Perimeter of a Right Angle Triangle
The perimeter of a right triangle is equal to the sum of its three sides. It is the sum of the right triangle's base, height, and hypotenuse. For example, the area of a right triangle ABC with sides AB, AC, and BC, the perimeter is equal to the sum of the sides BC + AC + AB = (a + b + c) units. The perimeter has a length unit and is a linear value.
Area of a Right Angle triangle
The spread, or the amount of space filled by a right triangle, is determined by its area. It is equal to half of the product of the triangle's base and height. Because it is a two-dimensional variable, it is expressed in square units. The base and altitude are the only two sides required to determine the right-angled triangle area.
The area of a right triangle may be calculated using the right triangle definition: A right triangle's area is equal to (1/2 * base * height) square units.
Conclusion
Now you get a right-angle triangle ACB. The angle made at point C is of 90degree. The triangle constructed is as per the measurements given in the question. So, now we are clear about the fact that the longest side of a right-angle triangle is the hypotenuse of the triangle. The two angles, other than that of 90degree in a right angle triangle, are always acute angles, which means, they are always less than 90degree. Obtuse angles that are an angle of more than 90 degrees are never formed in a right-angle triangle. While constructing a right-angle triangle, make sure to use the ruler and compass properly for adequate measurements.
FAQs on Right Angle Triangle
1. What are the types of right-angled triangles?
One of the angles of a right triangle is 90o, as we know. As a result, the triangle's other two angles will be acute angles. Isosceles right triangles and scalene right triangles are two types of special right triangles. The triangle having both the other two angles equal is referred to as an isosceles right triangle, and the triangle with the other two angles having different values is called a scalene right triangle.
2. What is the Isosceles right triangle?
A 90o-45o-45o triangle is an isosceles right triangle. For example, Consider a triangle ABC with sides AB, AC, and BC. Triangle ABC has an angle A of 90 degrees, making it a right triangle by definition. AB = AC; the triangle is also an isosceles triangle because the two sides are equal. The base angles are equivalent because AB = AC. We know that the sum of a triangle's angles is 180 degrees. As a result, the base angles sum up to 90o, implying that they are each 45o. As a result, the angles of an isosceles right triangle will always be 90o-45o-45o.
3. What is the Scalene right triangle?
A scalene right triangle is one in which one of the angles is 90 degrees and the other two angles are of varied measures up to 90 degrees. For example, consider a triangle PQR with sides PQ, PR, and QR, where PQ and QR are not equal. If Q = 90o in the triangle PQR, it is a right triangle. It is a scalene triangle since PQ is not equal to QR. A scalene triangle 30o-60o-90o is a specific example of a right triangle in which the ratio of the triangle's longest side to its shortest side is 2:1. The shortest side is the one on the other side of the 30o angle.
4. What are some tips and tricks related to right-angled triangles?
Some of the most important right triangle tips and tricks are listed here.
The Pythagoras theorem will always be satisfied when the side lengths are measured.
The hypotenuse is the side of a right triangle that is opposite the right angle and is the triangle's longest side.
The other two legs are perpendicular to each other; the base is one and the height is the other.
The perimeter of a right triangle is equal to the sum of its three sides' lengths.
5. Where can I find the notes on right-angled triangles?
Vedantu provides notes and questions on right-angled triangles. It covers topics such as right-angle triangle properties, different types of right-angled triangles, formulas, and more. Professional educators create content that is easy for students to learn and remember. Vedantu also offers study materials and a variety of competitive exams to students in grades 1 through 12. The contents contain notes, important topics and questions, revision notes, and other stuff. On Vedantu, you may access all of these resources for free. To access any of these resources, students must first register on the Vedantu website. You may also join up using the Vedantu smartphone app.
6. Can you explain in detail about acute, right and obtuse angle triangles for better clarification between the three?
The major difference between acute, right, and obtuse angle triangles is the angle made by the two adjacent sides of the triangle.
Acute Angle Triangle – when the angle formed between the two adjacent sides of the triangle is less than 90degree, it is known as acute angle triangle
Right Angle Triangle – when the angle formed between the two adjacent sides of the triangle is equal to 90degree, it is known as the right-angle triangle.
Obtuse Angle Triangle – when the angle formed between the two adjacent sides of the triangle is of more than 90degree, then it is known as the obtuse angle triangle.
7. what is a polygon and a regular polygon? In which category can we classify a triangle?
A polygon is a two-dimensional or plane shape that has straight sides. A polygon should at least have 3 sides and angles, not necessarily equal to each other.
On the other hand, a Regular polygon has all equal sides as well as all equal angles. The triangle is considered a polygon because it has three sides and angles. It is not always necessarily a regular polygon. Only equilateral triangles can be considered as regular polygons as they have equal sides and equal angles.
8. What is a Hypotenuse? Does only the Right-Angle Triangle have Hypotenuse?
The largest side in a right-angle triangle is called the hypotenuse. Since it is always opposite to the right angle, you must know that only right-angle triangles must have a hypotenuse and not the other types of triangles.
