The trilateral lengths a, B and C of △ ABC satisfy a + B = 8, ab = 4 and C2 = 56. Try to judge the shape of △ ABC and explain the reason

The trilateral lengths a, B and C of △ ABC satisfy a + B = 8, ab = 4 and C2 = 56. Try to judge the shape of △ ABC and explain the reason

The shape of ∵ a + B = 8, ∵ (a + b) 2 = 64, A2 + B2 + 2Ab = 64, ∵ AB = 4, ∵ A2 + B2 = 64-2ab = 64-8 = 56 = C2, ∵ ABC is a right triangle

If we know three numbers a, B and C and satisfy a + B = 252, B + C = 197 and C + a = 149, then a=______ ，B=______ ，C=______ ．

Because a + B = 252, B + C = 197, C + a = 149, so a + B + B + C + C = 2A + 2B = 2C = 252 + 197 + 149 = 598, then a + B + C = 598 △ 2 = 299, then a = 299 - (b + C) = 299-197 = 102, B = 299 - (c + a) = 299-149 = 150, C = 299 - (a + b) = 299-252 = 47, so the answer is: 102; 150; 47

There are three numbers ABC, a + B = 252, B + C = 197, C + a = 149?

A+B=252,B+C=197,C+A=149
The left and right are added separately
A+B+B+C+C+A=252+197+149
2(A+B+C)=598
A+B+C=299
Subtract the above three equations respectively
C=47,A=102,B=150

In the triangle ABC, if the maximum angle a is twice the minimum angle c, and the three sides a, B and C are three consecutive integers, then the value of a is?

Because the angle a is the largest, so the edge a is the largest (big angle to big edge), there is a sine theorem a / Sina = C / sinc, let a = x B = X-1, C = X-2, so a / C = Sina / sinc, because a = 2c, so Sina / sinc = 2cosc, so a / C = 2cosc, COSC = 1 / 2 * x / (X-2). Formula 1 has a cosine theorem COSC = (a ^ 2 + B ^ 2-C ^ 2) / (2Ab) with

Given that point ABC is on the same number axis, the number corresponding to point a is - 3, the distance between point a and point B is 4 unit lengths, and the distance between point a and point C is 7
How many unit lengths is the distance between point B and point C?

If the distance between point a and point B is 4, the number represented by point B is - 7 or 1;
If the distance between point a and point C is 7, then the number of point C is 4 or - 10,
So the distance between point B and point C may be:
-7 to 4: 11 unit length; - 7 to - 10: 3 unit length; 1 to 4,3 unit length; 1 to - 10,11 unit length
So the distance between B and C is 3 or 11

In triangle ABC, if the length of three sides is a continuous integer and the maximum angle is twice the minimum angle, what are the lengths of three sides?

According to the sine theorem
a/sinA=b/sinB=c/sinC
Let B = a + 1, C = a + 2, C = 2A
A * sinc = C * Sina
A * sin2a = (a + 2) Sina and sin2a = 2sinacosa
Cosa = (a + 2) / 2A
According to the cosine theorem
cosA=(b＾2+c＾2-a＾2)/2bc b=a+1 c=a+2
A ＾ 2-3a + 4 = 0, a = 4
b=5 c=6

It is known that all three sides of △ ABC are positive integers, a is equal to 5, B ≤ a ≤ C. how many triangles are there that meet the conditions? Try to write their lengths

b=1,2,3,4,5
The sum of the two sides of a triangle is greater than the third side
Prime factor
1,5,5
2,5,5
2,5,6
3,5,5
3,5,6
3,5,7
4,5,5
4,5,6
4,5,7
4,5,8
5,5,5
5,5,6
5,5,7
5,5,8
5,5,9

a. B, C are positive numbers not equal to 1, and Ax = by = CZ, 1 x + 1 y + 1 z = 0, find the value of ABC

Let AX = by = CZ = t, ∧ x = logat, y = logbt, z = logct, ∫ 1x + 1y + 1z = 1logat + 1logbt + 1logct = logta + logtb + logtc = logtabc = 0, ∧ ABC = t0 = 1, that is, ABC = 1

It is known that 3 / 3 x = 4 / 4 y = 6 / 6 Z is not equal to 0. Find the value of XY + YZ + ZX of X + y + Z

Let 3 / 3 x = 4 / 4 y = 6 / 6 z = k, x = 3k, y = 4K, z = 6K. ∵ 3 / 3 x = 4 / 4 y = 6 / 6 Z is not equal to 0 ∵ X / 9 = Y16 = Z / 36 = k, ∵ x + y + Z) / (9 + 16 + 36) = k, XY + YZ + ZX = 12K + 24K + 18K = 54K, ∵ XY + YZ + ZX = 54K / k = 54

Given an isosceles triangle, ab = AC, angle B = 22.5 ° and ab = 2A, calculate the area and perimeter of the triangle

Do the oblique height on AB, the outer angle is 45 degrees, and you can get the area (root 2 + 1 times a square)
Then we use Pythagorean theorem to find the hypotenuse, and then add it to get the perimeter