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Applications of Right Angled Triangles in Math

Right Angled Triangles, trigonometry graphs, mathematical theorems, Pythagorean triples, different types of right triangles

Right Angled Triangles

A right-angled triangle has a right angle as one of the angles which is the greatest angle of that triangle. Many problems in mathematics involve right triangles. Some of the important branches of mathematics which involve right triangles in their concepts are geometry and trigonometry. In geometry, when dealing with triangles, quadrilaterals and providing proofs for theorems require the knowledge of right triangles and their properties.


Trigonometry is one of the most important applications of mathematics with the utmost use of right triangles. For example, when drawing the trigonometry graphs, the values of x and y coordinates are represented by the line segments which form a right triangle after connecting with each other. Trigonometry is generally used for indirect measurement such as determining large distances or lengths by using measurements of angles and lengths of the sides of right triangles.

In trigonometry, for acute angles, the values of trigonometric functions can be represented and defined using the ratio of sides of a right triangle. For any given angle, a right triangle can be constructed with that given angle and the sides can be labeled based on the right angle and the given specific angle. These trigonometry functions are useful in different situations of daily life. For example, finding the height of a tower, the shadow of a tower, the height of the hill, or tree with the help of the angle of inclination with the observation point.


The angle of inclination can be categorized into two types with respect to the observation point and the direction of the object in which the observer is heading. If the observer is looking at the final object above the head point, then the angle included at this moment is called the angle of elevation. If the observer is looking at the final object which is located on the ground, then the angle at the point of observation towards the ground point is called the angle of depression.

Different Theorems

In math, different theorems exist to prove various axioms related to right triangles. One of the important theorems is the Pythagoras theorem. This theorem helps in finding whether the given group of three numbers form a right triangle or not. And the set of three numbers which form a right triangle when considered as the measurements of sides called Pythagorean triples. These concepts are used in many places while solving questions related to geometry.

There are different types of right triangles namely isosceles right triangle and scalene right triangle. If two angles are equal in the right triangle, then it is called the isosceles right triangle. These types of right triangles are very popular in the manufacturing works that are used by carpenters, architects, engineers, and graphic designers in developing their designs as well as construction work. When considering the sides of a triangle, if all the three sides of a right triangle are different, then it is referred to as the scalene right triangle. However, the right triangle will be having exactly one right angle in both cases and the remaining angles must be acute angles.

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