In Geometry, a triangle is a two-dimensional shape with three sides. A triangle is a polygon with least number of sides. The two sides of a triangle are joined end to end to form the vertex, and the angles of a triangle are formed between sides. Based on the measurement of sides and angles, the triangles are classified into different types. Based on the side length, the triangles are classified as a scalene triangle, isosceles triangle and an equilateral triangle. Based on the angle measures, the triangles are classified into an acute triangle, obtuse triangle, and right triangle. Now, let us discuss in brief about these different types of triangles:

- Scalene Triangle – All the three sides have different measurements.
- Isosceles Triangle – Two sides of a triangle are of the same length.
- Equilateral Triangle – All the three sides of a triangle have the same length.
- Acute Triangle – All the three angles are less than right angles.
- Obtuse Triangle – A triangle with one of its angles greater than a right angle.
- Right Triangle – One of the angles of a triangle is equal to 90 degrees (Right angle).

All these types of triangles have many applications in Mathematics and many other fields. In Mathematics, some important concepts like trigonometry, Pythagoras theorem, etc. are majorly dependent on the concept of right triangles. As we know, trigonometry is one of the branches of Mathematics which involves the study of the relationship between the sides and angles of a right-angle triangle. The trigonometry basics are majorly dependent on the right triangle. The three basic ratios are sine, cosine and tangent. Based on these three ratios, the other three ratios, such as cosecant, secant and cotangent are derived, which are the reciprocal of the sine, cosine and tangent functions respectively. The ratios are expressed in terms of the sides of a right triangle for the specific angle.

The right triangle is considered as one of the most important shapes in Mathematics. As we know, the right triangle can be classified into an isosceles right triangle and scalene right triangle. The isosceles right triangle consists of one right angle, and the other two angles are equal to 45 degrees. The scalene right triangle consists of one right angle and two unequal angles. It should be noted that the triangle has many types. But all the types of triangles must satisfy the angle sum property of a triangle. The angle sum property of a triangle states that the sum of interior angles of the triangle adds up to 180 degrees.

Right triangles are used in the construction as it helps to design the perfect corners. Architects use the Pythagoras theorem while designing the buildings. We know that the Pythagoras theorem states that the sum of the squares of the length of the legs is equal to the square of the longest side, which is called the hypotenuse of a right triangle.

For instance, if an architect wants to construct a square-shaped building, they will split the shape into two or more triangles. If any side lengths are not known, it can be easily found with the help of Pythagorean theorem. The three positive integers that satisfy the concept of Pythagoras theorem is called the Pythagorean triples. For example, if “a” is the perpendicular side, “b” is the base and “c” is the hypotenuse of the right triangle, then the Pythagoras triples are represented by (a, b, c). The smallest triples that satisfy Pythagorean theorem is (3, 4, 5), which is the scalene right triangle.

Right triangles play a vital role in many fields such as navigation, astronomy, and so on. Egyptians use the concept of right triangles to design the pyramids. The right triangle is used to find the length or the distance between two things. Right triangle trigonometry can be used to measure the distance which cannot actually be measured. For example, if we need to find the distance between the sun and the moon, the distance will be measured with the help of the law of sines. Generally, to find the length or the distance between two things, the angle of depression, angle of elevation, etc., are required. Right triangles are generally used by the carpenters, surveyors to ensure the square corners.