In the triangle ABC, C = 3 / 4 π, Sina = 5 / 5 root sign, find cosa and SINB, if AB = 2 times root sign 2, find a, B

According to C = 3 π / 4 > π / 2, triangles are obtuse triangles, and a and B are acute angles. Sina = √ 5 / 5cosa = √ (1-sin ^ 2a) = √ (1-1 / 5) = 2 √ 5 / 5sinb = sin (π - C-A) = sin (π / 4-A) = sin π / 4cosa cos π / 4sina = √ 2 / 2 [cosa Sina] = √ 2 / 2 [2 √ 5 / 5 - √ 5 / 5] = √ 10 / 10

In the triangle ABC, angle a is less than or equal to angle c is less than or equal to angle B, and 2 angle B is equal to 5 angle a, the value range of angle B is calculated
Such as the title

2A less than or equal to B + C plus a 3A less than or equal to a + B + C, that is 3A less than or equal to 180 a less than or equal to 60 5A less than or equal to 300 2B less than or equal to 300 b less than or equal to 150 greater than 0

In RT triangle ABC, if AB = AC + 22, BC = 44, then AC=
This is a topic in the feedback of the eighth class

33 AB-AC=22.AB2=BC2+AC2 (AB-AC)(AB+AC)=44*44
Instead, we need to work together

Sine theorem and application conditions, cosine theorem and application conditions

The content of sine theorem is that in △ ABC, if the edges opposite angles a, B and C are a, B and C respectively, then a / Sina = B / SINB = C / sinc = 2R (where R is the radius of triangle circumcircle)
Application fields of sine theorem
In solving triangles, there are the following applications
(1) given the two corners and one side of the triangle, solve the triangle
(2) given the angles of the two sides and one side of the triangle, we can solve the triangle
(3) using a: B: C = Sina: SINB: sinc to solve the transformation relationship between angles
The ratio of the opposite side to the hypotenuse of an acute angle of a right triangle is called the sine of the angle
Cosine theorem
Cosine theorem is an important theorem to reveal the relationship between the sides and angles of a triangle. It can be directly used to solve the problem of finding the third side or finding the angle of three known sides of a triangle. If the cosine theorem is transformed and appropriately transferred to other knowledge, it will be more convenient and flexible to use
Specific usage: http://baike.baidu.com/view/147231.htm

】How to use sine theorem to judge how many solutions a triangle has?
I don't know what a > bsina two solutions, a = bsina one solution, a

Sine theorem a / Sina = B / SINB asinb = bsina and 0 < B < 180
A solution of SINB = 1 and SINB = 90 ° when a = bsina
a> When bsina, 0 < SINB < 1 and 0 < B < 180 ° B may be acute angle or obtuse angle
a

How can we see that there are several solutions to the triangle according to the sine theorem?
According to the given conditions, the diagonal of two sides and one side

Draw a figure to know, in a triangle, let the three sides be ABC, where the side length AB and angle a are known
A is less than B & nbsp; sin & nbsp; a & nbsp; has no solution
A less than or equal to B & nbsp; & nbsp; has no solution
A solution of a = B & nbsp; sin & nbsp; a & nbsp
A solution of a greater than B
The other two solutions
(there are only three cases of no solution, one solution and two solutions)

How to judge the number of solutions of triangle in sine theorem?
Is the opposite side of the big corner big? But it seems that it is not
It seems that there are exceptions when doing the questions, for example: triangle ABC, ab = 10 times root 2, a = 45 degrees, when BC = 20 times root 3, what is the angle of C?

The largest edge is the biggest angle, the second largest edge is the second largest angle, and the smallest edge is the smallest angle

On the sine theorem in the triangle... Help···
In the triangle ABC, given the angle a = 60 ° and the side BC = 2 √ 3, let the angle B = x and the perimeter of the triangle ABC be y
【1】 Find the analytic expression of the function y = f (x), and write out the function domain
【2】 Finding the range of function y = f (x)

1)
AC=BC*sinx/sinA=4sinx
AB=BC*sin(180-60-x)/sinA=4sin(120-x)
Y=2√3+4sinx+4sin(120-x)
=2√3+8[sin60*cos(60-x)]
=2√3+4√3cos(60-x),
0

The problem of triangle sine theorem
A = x, B = 2, B = 30 ° what is the value of x 1.2. There is a solution 3. There are two solutions, that is, the range of values when there are several solutions to X. three questions are a / Sina = B / SINB = C / sinc
I know this. When I say what value x takes, I mean the value of X, that is, how much is a~

Because angle B is an acute angle

Mathematics compulsory five sine definite understanding triangle
In △ ABC, we know that B = √ 2, C = 1, B = 45 ° and find a, a, C
[calculation process. Thanks]

Note: "root 6" refers to the calculation result of "root 6 under the quadratic root sign". According to the sine theorem: B / SINB = C / sinc, sinc = 1 / 2 can be obtained. Because b > C, angle b > angle c, angle c = 30 ° because a + B + C = 180 ° so angle a = 105 ° because Sina = sin105 ° = sin (60 ° + 45 °) = sin60 ° cos45 ° +

In the triangle ABC, C = 3 / 4 π, Sina = 5 / 5 root sign, find cosa and SINB, if AB = 2 times root sign 2, find a, B