**branch of mathematics**related to the

**measurement of the sides and angles of triangles**. According to its etymology, formed by the words τριγωνο “trine” and μετρον “metron”, trigonometry means “measurement of triangles”.

**triangles are found everywhere**in the world we live in.

It is of great importance to learn trigonometry in secondary and high school education, as it helps us to understand the known reality much better.

Index

### What is trigonometry?

Trigonometry is made up of different **theorems and laws** . These theorems and laws dictate how the angles and sides of triangles must be calculated.

The **Pythagorean Theorem** is one of the most important, and it applies to right triangles, that is, triangles that have an angle of 90 degrees, also called a right angle. Indicate, by means of a formula, that there is a relationship between the two sides that form the right angle (legs) and the longest side, which opposes the angle (hypotenuse). The formula is:

**c ^{2} = a^{2} + b^{2}**

The square of the hypotenuse is equal to the sum of the squares of the legs.

The **theorem Such** indicates that certain conditions are met, two triangles can be similar. The so-called **criteria of similarity** are based on the sides and angles of both triangles in question. If some of these sides and angles coincide between triangles, the triangles are similar.

The **Laws of Sines and Cosines** are two laws that relate the sides and angles in the same triangle, in order to calculate the measures of those missing sides and angles. They are similar to the Pythagorean Theorem, but are characterized by acting on triangles that are not right.

## What is trigonometry for?

Trigonometry is used to measure distances in triangular formations. Its use can be traced to the civilizations of the Babylonians, Egyptians, Greeks and perhaps other ancient cultures. It is a fundamental part of analytical geometry, which studies geometric figures.

Trigonometry was widely used in navigation by means of a tool called a **sextant** , with which distances were measured by triangulating with the stars.

Currently, this measurement technique is most used in outer space, and it is one of the best for calculating and estimating colossal measurements.

In civil engineering, it is used to determine heights of posts, according to the angle that would form between the tip and the end of their shadow; also to calculate inclinations of platforms, according to the angles that these form with the floor.

The ancient Egyptians used simple machines during the construction of the pyramids, in which they used trigonometry to a great extent. A 45 degree angle applied on an inclined plane cuts the effort to slide any object over it by half.

### Trigonometry serves purposes such as:

- Measuring angles with two known sides
- Measure Sides with Known Angles
- Know the distances between three points during a navigation
- Observe if two triangles are similar, that is, they have equal angles but similar sides
- Estimate algebraically how long one side of a triangle is

### What is used in trigonometry?

Trigonometry requires the use of tools to solve the triangles. As we have already mentioned, in triangles the angles and the length of the sides are measured.

For a correct calculation of the triangles, the following will be used:

**Protractor:**It is a semicircular or circular tool that has a scale to measure angles. If it is semicircular, the scale will range from 0 ° to 180 °. If it is circular, it will span from 0 ° to 180 ° in its upper half and from 181 ° to 360 ° in its lower half.**Ruler:**It is a tool for measuring lengths that can have very varied scales. The ruler is a straight bar whose most common scale ranges from 0 to 30 centimeters.**Squares: Squares**are triangular tools for measuring lengths, and there are two types: Squares with angles of 60 °, 30 ° and 90 °. Angle brackets with 45 °, 45 ° and 90 ° angles.**Scientific calculator:**It is an electronic device that is responsible for calculating the relationships between the sides and angles of triangles in trigonometry, among other numerous functions.

Dr. Samantha Robson ( CRN: 0510146-5) is a nutritionist and website content reviewer related to her area of expertise. With a postgraduate degree in Nutrition from The University of Arizona, she is a specialist in Sports Nutrition from Oxford University and is also a member of the International Society of Sports Nutrition.