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The ratio of the side length of a triangle is 3:4:5. It is known that the circumference of this triangle is 48 cm. The circumference of this triangle is 48 cm, and the longest side of the triangle is 48 cm How much is it?
It was divided into 12 parts, 48 / 12 = 4cm
So the three sides are 12cm 16cm 20cm
The longest 20cm
What are the three sides of this triangle which are 48 cm and 5 cm long?
5+4+3=12
Longest side = 48 / 5 △ 12 × 5 = 4cm
The shortest side = 48 / 5 / 12 × 3 = 12 / 5 cm
There is also one side = 48 in the 5th △ 12 × 4 = 16cm in the 5th
The ratio of three sides of a triangle is 3:4:5. Given that the circumference of the triangle is 48 cm, what is the longest side length?
20CM
It is known that the three sides of obtuse triangle are a, a + 1 and a + 2 respectively, where the maximum internal angle is not more than 120 ° to find the value range of real number a
∵ the three sides of the triangle are a, a + 1, a + 2,
If the length of the three sides of an obtuse triangle is a + 1, a + 2, a + 3, then the value range of a is______ .
∵ the three sides of obtuse triangle are a + 1, a + 2, a + 3,
The angle of a + 3 pair is obtuse angle, which is set as α,
∴cosα=(a+1)2+(a+2)2−(a+3)2
2(a+1)(a+2)=a−2
2(a+1)＜0，
The solution is: - 1 < a < 2,
From a + 1 + A + 2 > A + 3, a > 0,
Then the value range of a is 0 < a < 2
So the answer is: 0 < a < 2
In the obtuse triangle ABC, if 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 the obtuse triangle ABC, a = 1, B = 2,
According to cosine theorem, COSC = A2 + B2 − C2
2ab=1+4−c2
4＜0，
The solution is as follows:
5＜c＜3，
Then the range of the maximum edge C is（
5，3）．
Therefore, B
In an obtuse triangle, a = 1, B = 2, 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 > radical 5
Because a + b > C, C < 3
3 > C > root 5
Let a, a + 1, a + 2 be the three sides of an obtuse triangle, then the value range of a is?
Then the angle to which a + 2 is directed should be the maximum angle c, so COSC = (a + 1) 2 + a 2 - (a + 2) 2
Under the condition of 0 ＜ x ＜ 1 and 0 ＜ y ＜ 1, the probability that three line segments of length x, y and 1 can form an obtuse triangle is obtained by taking any two numbers of X and y
The condition of forming a triangle is x + Y > 1, and the probability of forming an obtuse triangle is x 2 + y 2
From the five line segments with length of 1,2,3,4,5, if any three of them are selected as edges, the probability of forming an obtuse triangle is______ .
From the five line segments of length 1, 2, 3, 4, 5, take any three, all cases have C
Three
Five
=10 kinds,
When the three sides can form an obtuse triangle, the cosine value of the largest side must be less than zero, that is, the sum of squares of the smaller two sides is less than the square of the third side,
Therefore, there are only 2, 3, 4 and 2, 4, 5 to form an obtuse triangle,
Therefore, the probability of forming obtuse triangle is 2
10=1
5，
So the answer is 1
5．
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