The first thing that we are going to do before entering fully into the establishment of the meaning of the term acute angle is to know the etymological origin of the two words that give it form:
-Angle, first of all, derives from the Greek. Specifically, it emanates from “ankulos”, which can be translated as “bent” and later became Latin as “angulus”, where it already takes the meaning of “angle”.
-Agudo, on the other hand, has its origin in Latin, exactly in the word “acutus”, which is synonymous with “acute”. That in turn comes from the verb “acuere”, which is synonymous with “sharpen”.
Two rays that share the same vertex as the point of origin form an angle. According to the characteristics that are analyzed, it is possible to differentiate between multiple types of angles.
According to DigoPaul, an acute angle is an angle that measures more than 0º and less than 90º. This means that, if we only consider the integers, an acute angle measures between 1º and 89º.
This definition of the measures of acute angles allows us to affirm that these are angles greater than null angles (whose measurement is equal to 0º) but less than right angles (90º), obtuse angles (more than 90º and less than 180º), the flat angles (180º) and the perigonal angles (360º).
Continuing with the classifications of acute angles, we can highlight that they belong to the set of convex angles, which encompasses all angles with measurements greater than 0º and less than 180º, unlike concave angles (which measure more than 180º and less 360º).
It is possible to find acute angles in different geometric figures. In right triangles, two acute angles and one right angle appear. The obtuse triangles, meanwhile, have two acute angles and one obtuse angle. In the case of acute triangles, the three interior angles in the figure are acute angles.
We can also notice sharp angles in objects or elements of everyday life. The most common way to cut the pizza is into triangular pieces: in each slice we can find three acute angles.
In addition to all the above, we can indicate that in order to measure an acute angle, it is necessary to resort to the use of a protractor. This article can be of two main forms: with a semicircular shape, to be able to measure angles of a maximum of 180º, or with a circular shape. The latter is used to measure approximately any type of angle, since its maximum is at 400º.
In the same way, we cannot overlook the fact that certain mathematical and trigonometric operations can be performed with acute angles in triangles. Thus, for example, the sine can be calculated, which will be the result of the quotient between the length of the leg opposite the angle and the hypotenuse.
And this without forgetting that, in addition, you can proceed to calculate the cosine, tangent, secant, cosecant and cotangent.