There are four line segments with the length of 1.2.3.4 respectively. The probability that any three of them will form a triangle is

There are four line segments with the length of 1.2.3.4 respectively. The probability that any three of them will form a triangle is

There are three out of four cases: C (4,3) = 4
As long as there is 1, it must not form a triangle, that is, only 2, 3 and 4 can match
Probability: 1 / 4

Among the five line segments with lengths of 1, 2, 3, 4 and 5, the probability that the three line segments taken out are edges and can form an obtuse triangle is __

Take any three of the five line segments with lengths of 1, 2, 3, 4 and 5 respectively. There is C in all cases
three
five
=10 kinds,
Among them, when the extracted three sides can form an obtuse triangle, the cosine value of the largest side must be less than zero, that is, the sum of the squares of the smaller two sides is less than the square of the third side,
Therefore, there are only two methods to form obtuse triangle: 2, 3, 4 and 2, 4 and 5,
Therefore, the probability that the extracted three line segments are edges and can form an obtuse triangle is 2
10=1
5，
So the answer is 1
5．

Under the conditions of 0 ＜ x ＜ 1 and 0 ＜ y ＜ 1, take any two numbers of X and y, and find the probability that three line segments with lengths of X, y and 1 can form an obtuse triangle

The condition of forming a triangle is x + Y > 1, and the probability of forming an obtuse triangle is X ²+ y ²

Let a, a + 1 and a + 2 be the three sides of an obtuse triangle, then the value range of a is?

Then the angle opposite a + 2 should be the maximum angle c, so COSC = (a + 1) ²＋ a ²－ (a＋2) ²

In an obtuse triangle, a = 1, B = 2, and C is an obtuse angle. Find the value range of C

c^2=a^2+b^2-2abcosC
A ^ 2 + B ^ 2-C ^ 2 / 2Ab = COSC because of the obtuse angle of C, COSC < 0
So 5-c ^ 2 < 0
c^2-5＞0
C > root 5
Because a + b > C, C < 3
3 ＞ C ＞ root 5

In the obtuse triangle ABC, a = 1, B = 2, then the value range of the maximum edge C is () A. （ 3，3） B. （ 5，3） C. （2，3） D. （ 6，3）

∵ in obtuse triangle ABC, a = 1, B = 2,
Obtained from the cosine theorem: COSC = A2 + B2 − C2
2ab=1+4−c2
4＜0，
Solution:
5＜c＜3，
Then the range of the maximum edge C is（
5，3）．
Therefore: B