Introduction to Trigonometry

Acute Angle

Introduction to Acute Angle

An acute angle refers to an angle that is less than 90 degrees, but larger than zero degrees. Therefore, it is an angle that measures less than a right angle. Acute angles are certainly sharp angles.

They are more drastic than a right angle or an obtuse angle. Furthermore, one can add two or more acute angles so as to equal the right angle. Learn more about acute angles here.

acute angle

What is an Acute Angle?

An acute angle consists of two rays or line segments. Furthermore, these rays or line segments intersect at one endpoint of an acute angle. One line segment is below, while the other is above.

Most noteworthy, an acute angle is smaller than 90 degrees. Also, the angle construction and measurement can take place with the help of a protractor.

Acute angles are certainly sharp angles. They are more drastic than a right angle or an obtuse angle. Furthermore, one can add two or more acute angles so as to equal the right angle.

Calculation of Acute Angle

A right triangle refers to any triangle which has a 90 degree or right angle. Furthermore, the angles in any triangle must total 180 degrees. This certainly means that the other two angles are acute.

Trigonometry primarily concerns itself with the measurements and ratios of right triangles. Most noteworthy, sine, cosine, and tangent centre on the acute angles of a right triangle. Hence, one must use these ratios to calculate the angles.

An individual must orient the triangle such that one leg of the right angle becomes vertical. Furthermore, the individual must label this leg as “a”.

The other leg of the right angle would be horizontal. The individual must label this leg as “b”. The third side which is the hypotenuse must be labelled “c”.

The individual must then measure the length of the three sides. Moreover, there exist applications, which allow the measurements of sides “a” and “b”. In such a case, the individual must make use of the Pythagoras Theorem for calculating side “c”.

The individual must divide the length of side “a” with the length of the hypotenuse, side “c”. This is certainly the sine of the acute angle which shares the horizontal leg with the right angle.

Moreover, the individual must enter this ratio into the scientific calculator. Then the individual must make use of the inverse sine function for the determination of the angle.

The individual must enter 90 degrees to this angle. Also, the individual must subtract the result from 180. Finally, this would be the value for the second acute angle existing in the right triangle.

Acute Angle in Real Life and Acute Angle Examples

Geometry certainly exists all around. Most noteworthy, there are real-world examples of acute angles appearing all around us. Below are the various arenas of everyday life where acute angles appear:

In the Classroom- There are plenty of examples of acute angles in the classroom. Examples include a folding easel, a pencil tip, number 7, and the top of letter A.

Furthermore, there exist many examples of student-made art which contain acute angles. Moreover, the letter K and each tip of football are acute angles.

On the Road- Modern architectural designs and structures contain acute angles. These acute angles certainly add various shapes and add interest and attractiveness.

Moreover, a yield sign contains three angles. Also, an exit ramp creates an acute angle when it swerves from the highway. Furthermore, arrows on road signs such as “one way” and “no right turn” display acute angles.

Solves Question for You

Q1. Which of the following statements related to acute angles is wrong?

A. Acute angle is less than 90 degrees
B. Acute angle is more than 90 degrees
C. Acute angle is larger than 0 degrees
D. Acute angle measures less than a right angle

A1. The correct answer is option B. which is an acute angle is more than 90 degrees. This is because an angle more than 90 degrees is obtuse angle and not acute.

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