An acute angle measures less than 90º and more than 0º.
The first thing we are going to do before entering fully into establishing the meaning of the term acute angle is to know the etymological origin of the two words that give it shape:
– Angle , first of all, derives from Greek. Specifically, it emanates from ankulos , which can be translated as "bent" and which later passed into Latin as angulus , where it now takes on the meaning of "angle."
– Acute , 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."
What is an acute angle
Two rays that share the same vertex as their point of origin form an angle . Depending on the characteristics analyzed, it is possible to differentiate between multiple types of angles.
An acute angle is an angle that measures more than 0º and less than 90º . This means that, if we only consider integers , an acute angle measures between 1º and 89º.
It is possible to find acute angles in different geometric figures.
Other classifications
This definition of the measurements of acute angles allows us to affirm that they are angles greater than null angles (whose measure is equal to 0º) but less than right angles (90º), obtuse angles (more than 90º and less than 180º), plane angles (180º) and 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).
Acute angles in different figures and objects
It is possible to find acute angles in different geometric figures. In right triangles , two acute angles and one right angle appear. Obtuse triangles , on the other hand, have two acute angles and one obtuse angle. In the case of acute triangles , the three interior angles of the figure are acute angles.
We can also notice acute angles in objects or elements of everyday life. The most common way to cut pizza is into triangular slices: in each slice we can find three acute angles.
In addition to all of the above, we can indicate that in order to measure an acute angle it is necessary to use a protractor . This article can be of two fundamental shapes: 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.
Various calculations
In the same way, we cannot ignore the fact that certain mathematical and trigonometric operations can be performed with acute angles in triangles . Thus, for example, you can calculate the sine , which will be the result of the quotient between the length of the leg opposite the angle and the hypotenuse.
And that is without forgetting that, in addition, you can proceed to calculate the cosine , the tangent , the secant , the cosecant and the cotangent .