What is a Right Triangle & How is it related to Pythagoras Theorem?

Pythagoras Theorem

Right-angled triangles consist of three angles with any one of them equal to 90 degrees. In the third degree, all angles are right angles. The right triangle plays a significant role in trigonometry. Whenever two sides added together equals the same number of angles as the third side, the result is a triangle. For this reason, all closed figures with three sides and three angles equal to one have the property known as a triangle. Due to their closed nature, triangles can have a variety of shapes, each described by the angle formed between two adjacent sides. 

A right-angle triangle is defined as a pair of sides with an angle of 90 degrees between them. Right triangles can also be scalene triangles or isosceles triangles. A scalene right triangle will have unequal lengths for all the sides, but any one of the angles will be a right angle. A right triangle with an equal hypotenuse and base has the same length perpendicular and base sides. The hypotenuse has the third unequal side. Three sides make up a right angle: the height, the base, and the hypotenuse. The height of the triangle falls on the side opposite to the right angle. The length of the hypotenuse is the longest among all three sides.

Pythagoras theorem of a right-angled triangle:

This relationship between the triangular sides is explained by Pythagoras theorem. According to Pythagoras, the three sides of a right triangle have the following relationship:

Hypotenuse^2 = Perpendicular^2 + Base^2

Since the square of the length of the hypotenuse is equal to the sum of the squares of base and height, we can have the Pythagorean theorem. We can calculate the area of the biggest square by adding the squares of the two other small squares.

Properties of a right-angled triangle:

  • There is always one angle of 90° or right angle.
  • The hypotenuse refers to the side opposite the 90° angle.
  • As a rule, the hypotenuse is always on the longest side.
  • Summed together, the other two angles within the triangle equal 90°.
  • Base and perpendicular are the two remaining sides that surround the right angle.
  • The area of a right-angled triangle is equal to half of the product of adjacent sides of the right angle, i.e.,

Area of Right Angle Triangle = ½ (Base × Perpendicular)

  • Dropping a perpendicular from the hypotenuse to the right angle, we get three similar triangles.
  • The radius of the circle that passes through the hypotenuse of a triangle is equal to half of the circumcircle’s radius.
  • Triangles are defined as Isosceles Right Angled Triangles if there is one right angle 90°, the other two equal 45°, and the adjacent sides between 90° and 90° are equal.

Area of a Right-angled triangle:

The area of a triangle is measured in a square unit, corresponding to the amount of space occupied by a 2-dimensional object. To calculate the area of a triangle, two formulas can be used:

area= a×b/2 and where, 

Heron’s formula i.e. area= √s(s−a)(s−b)(s−c)

Where, s is the semi perimeter and is calculated as s = a+b+c/2 and a, b, c are the sides of a triangle.

The base of a right-angled triangle is always parallel to the height. If only angles are given and not sides, the area of the right-angled triangle can be calculated by the following formula:

Area= b×h / 2

The perimeter of a right triangle:

Right triangles, as we know, have three sides: Base, Perpendiculars, and Hypotenuses, so the perimeter of a right triangle is the sum of all its sides. 

Perimeter of right triangle = Length of (Base + Perpendicular + Hypotenuse)Pythagoras theorem formula can be easily understood with the help of Cuemath, one of the best maths learning websites for any person. The concepts are taught and explained very well by expert teachers.

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