In the triangle ABC, angle c equals 90 degrees. If angle a equals 45 degrees and C equals 2, find a and B

In the triangle ABC, angle c equals 90 degrees. If angle a equals 45 degrees and C equals 2, find a and B

a=b=√2a²+b²=2²2a²=4  a²=2  a=√2、b=√2

Let the opposite sides of the internal angle A.B.C of the triangle ABC be a.b.c. if the three sides b.a.c form an arithmetic sequence, 3sina = 5sinb, then the angle c is equal to?

sinA:sinB=5 :3
Then a: B = 5:3, then a: B: C = 3:4:5

Anhui 2013 college entrance examination penultimate condition B + C = 2A 3sina = 5sinc angle c good life safety!
3sina = 5sinb is wrong=

3sina = 5sinb: 3A = 5b, B = 3A / 5, C = 7a / 5, cosine theorem cos C = - 1 / 2, C = 2pi / 3

In the acute triangle ABC, we prove that tgatgb > 1

tan(A+B)=(tanA+tanB)/1-tanAtanB
A+B=180-C
∴tanAtanB=[(tanA+tanB)/tanC]+1
In acute triangle ABC
tanA>0
tanB>0
tanC>0
So tanatanb = [(Tana + tanb) / Tanc] + 1 > 1

The minimum value of the acute triangle ABC, atan, btanc is known

In triangles, tanatanbtanc = Tana + tanb + Tanc, and f (x) = TaNx is convex on (0, π / 2), so Tana + tanb + Tanc > 3tan ((a + B + C) / 3) = triple root 3
The equal sign holds if and only if a = b = C = π / 3, so the minimum value is 3 times the root sign 3

The acute triangle ABC proves that the multiplication of tanatanbtanc is greater than 1

Triangle ABC tanatanbtanc = Tana + tanb + Tanc
The proof is as follows
tanA=tan(∏-B-C)=-tan(B+C)=
-(tanB+tanC)/(1-tanBtanC)
=（tanB+tanC)/(tanBtanC-1)
So Tana * (tanbtanc-1) = tanb + Tanc
tanA*tanB*tanC - tanA=tanB+tanC
So tanatanbtanc = Tana + tanb + Tanc
To prove tanatanbtanc > 1, just prove Tana + tanb + Tanc > 1
Because ABC is an acute triangle, a, B and C are all greater than 0 and less than 90 degrees,
So Tana > 0, tanb > 0, Tanc > 0
Another reason is that at least one angle of a triangle is greater than or equal to 60 degrees,
So Tana > root 3, tanb > 0, Tanc > 0
So Tana + tanb + Tanc > radical 3 > 1
So tan atanbtan C > 1

If an internal angle of an isosceles triangle is 60 degrees and the side length is 18 cm, then the perimeter of the isosceles triangle is 60 degrees_____ cm

54

If the circumference of an isosceles triangle is 18cm and one side is 4cm, what are the lengths of the other two sides?

Judgment:
an isosceles triangle
1. If one side is 4 and the other side is 4, then the third side is 10. According to the sum of the two sides of the triangle is greater than the third side, 4 + 44,7 + 4 > 7,7-4 can be used

In order to know the triangle ABC, ab = AC, the middle line of a waist divides the circumference of the triangle into two parts of 21cm and 12cm, and calculates the waist length

Let waist length = 2x
The perimeter of the two parts is 3x, x + bottom edge
1.3x=21
If x = 7, the waist length is 14 and the bottom edge length is 5
2.3x=12
If x = 4, the waist length is 8 and the bottom length is 17, because 8 + 8

In the inscribed quadrilateral ABCD, if AB = BC = CD, AC is diagonal and ∠ ACD = 30 °, then ∠ CAD=

50°
Because AB = BC = CD, so angle CAD = BAC = ACB
Because of the arc of the pair, the diagonal complementation of the quadrilateral, the angle DAB + DCB = 180 degrees
Because CAD is 30 degrees, CAD = (180-30) divided by 3 = 50