What is the probability of a triangle being an acute angle, a right angle, and an obtuse angle

Take any point a on the circle, and a is the diameter n of the diameter m and the perpendicular m (i.e., the circle is divided into four equal parts).

It is assumed that it is divided into four parts: 1, 2, 3, and 4. The other two points A and B can make the triangle abc an acute triangle or a right triangle only in the opposite part (i.e., 1, 3 or 2, 4). It is not difficult to calculate the probability of this.

If the triangle ABC is a right triangle, one of its angles must be right angles, and the probability of right angles is 0.

If the angle c is a right angle, there are n ways to take point A, and point B has been determined (ab is the diameter) and point C has n-2 ways to take it.

There are n(n-1)(n-2) ways to take any three points on a circle.

Then the probability of taking three points and being at right angles is n(n-2) n(n-1)(n-2), and n approaches infinity with a probability of 0.

then the probability of an acute triangle is.

The probability of a right triangle is 0

The probability of an obtuse triangle is .

Actually, there's a good way, please see.

A triangle has at least two acute angles.

Up to one right angle or one obtuse angle.

Acute angle 18 36 1 2

Right and obtuse angles are 9 36 1 4, respectively

There is a probability of this... Take the picture out and say it...

A right triangle has one right angle, two acute angles, and no obtuse angles. A right triangle is a geometric figure, which is a triangle with a right angle angle, and there are two types: ordinary right triangle and isosceles right triangle.

In a right-angled triangle, the two sides adjacent to the right angle are called right-angled edges, and the edges opposite by right-angled angles are called hypotenuses. The sides of a right triangle that are opposite by right angles are also called "chords". If the two right-angled sides are not the same length, the short side is called the "hook" and the long side is called the "strand".

Triangle. There are only three corners. The sum of the inner angles is 180 degrees. So a triangle can only have one right angle, and the other two can only be acute angles.

Right triangle with 1 right angle, 2 acute angles, no obtuse angles.

According to the analysis, it can be seen that

A triangle with an angle that is an acute angle may be an acute triangle, a right triangle, or an obtuse triangle, so a triangle with an acute angle may be an obtuse triangle, which is true;

So the answer is:

From the analysis, it can be seen that there is a triangle with an acute angle, which may be an obtuse triangle;

So the answer is: true

Suppose the range of three numbers is (0,l), in the xyz coordinate system, we find a region in this cube of length l, satisfying that x,y,z are blind to form an acute triangle. Then put l to infinity and find the limit.

You might as well set z>x, z>y, then.

The constraint of an obtuse triangle is.

x^2+y^2z

At this time, a conical surface and a plain area are sandwiched.

The integral (dxdydz) integral interval is the above constraint and is all within (0,l). The obtained value must be approximate with l 3 to obtain a constant value. This value does not change when l tends to infinity. So first of all, make sure that the probability of an obtuse triangle is positive.

Then the above is to assume z>x, z>y

Then the actual three sides act as the largest edges and the cluster space are all equal probabilities, so multiplying the value obtained above by 3 is the probability of an acute triangle.

The probability of a right triangle is 0 because it is not a region, but a curve;

The probability of an obtuse triangle is also a positive value.

Finally, add to the probability that the triangle cannot be formed, and the sum of Zheng is exactly 1

There are at least (2) acute angles and a maximum of (1) right angles (or obtuse angles) in a triangle

In the triangular collision of a hole, if one angle is obtuse and one angle is acute, then the third angle is acute.

The triangle is three inner pei angles and 180 degrees.