In this publication, we will consider what an obtuse angle is, as well as analyze examples of tasks in which it is involved.
Angle detection
An angle is a geometric figure that consists of two rays emanating from one point.
A ray is a part of a straight line that comes from one point, this point is called the beginning of the ray. The beam has a beginning but no end.
An angle is a geometric figure consisting of two rays with a common origin. If this point, the point of origin of the rays, is denoted by the letter A, then the angle will be called angle A.
An angle can be called a single letter, by the name of the point from which the rays emanate.
If you put a point on the sides of the corner, for example, points B and C, then the corner can be called with three letters the angle BAC or the angle CAB, the point from which the rays emanate is always written in the middle.
Consider what types of angles can be on a plane.
Types of angle
- If angle A satisfies the condition 0 > Angle A < 90o, we call such an angle acute.
- If angle A = 90o, such an angle is called a right angle.
- If angle A satisfies the condition 180° > angle A > 90 ° , such an angle is called an obtuse angle.
- If the angle A \u003d 180 °, then such an angle is called deployed.
Definition of obtuse angle
Angle is dumbif its is between 90 and 180 degrees.
∠α – dumb if 90° α <180 °.
That is, an obtuse angle is greater than a right angle (90°), but less than a straight angle (180°).
Examples of tasks with obtuse angle
Task 1
Given a triangle with two known angles, 34° and 27°. Find the third one and determine if it is stupid.
Decision:
Let’s take the unknown value as “α“. As we know, the sum of the angles of a triangle is 180 degrees, which means:
α = 180° – 34° – 27° = 119°.
Therefore, the angle α – stupid.
Task 2
Given a rhombus, area (S) which is 12,5 cm2, and the length (a) sides – 5 cm. Find its angles and determine whether they are obtuse.
Decision:
The sine of the rhombus angle (α) can be found as follows (derived from the figure calculation formula):
Consequently, the α = 30° (arcsin 0,5), is acute.
As we know, the sum of adjacent angles of a rhombus is 180 degrees, so the second angle β equal to 150° (180° – 30°)and he is dumb.
