In the known triangle ABC, BC = x, AC = 2, B = 45 degrees, if the triangle has two solutions, then the value range of X is? (2,2√2) Draw an angle of 45 ° with B as the vertex and BC = x on one side Take point C as the center of the circle, radius 2, draw a circle, because there are two solutions, so the circle should intersect with the other side, if there is no solution, it is separated, if there is a solution, it is tangent After you draw the picture, you can clearly see that the distance from point C to the other side (the distance from the center of the circle to the chord), that is, the height of the triangle ABC is less than the radius, that is, xcos 45 ° < 2 In addition, BC edge is larger than radius, that is, x > 2 two

In the known triangle ABC, BC = x, AC = 2, B = 45 degrees, if the triangle has two solutions, then the value range of X is? (2,2√2) Draw an angle of 45 ° with B as the vertex and BC = x on one side Take point C as the center of the circle, radius 2, draw a circle, because there are two solutions, so the circle should intersect with the other side, if there is no solution, it is separated, if there is a solution, it is tangent After you draw the picture, you can clearly see that the distance from point C to the other side (the distance from the center of the circle to the chord), that is, the height of the triangle ABC is less than the radius, that is, xcos 45 ° < 2 In addition, BC edge is larger than radius, that is, x > 2 two

Because there are two solutions, the circle should intersect the other side
Because AC = 2, make a circle of radius 2 with C as the center
The point where an arc intersects a straight line on the other side is a,
If they are tangent, there is only one point of intersection, then there is only one case to determine the triangle ABC
If the circle intersects with the other side, then there are two intersections A1 and A2 between the circle and the side, and there are two cases of triangle ABC
A1bc and a2bc

In the triangle ABC, a = x, B = 2, angle B = 45 degrees, if the triangle has two solutions, then the value range of X is ()

From the question: because the triangle ABC has two solutions, so csin45 '< B < C, where ad is perpendicular to D through a, then ad = csin45 ° has two solutions, then the value of AC must be greater than ad, and the symmetry about AD can satisfy the two solutions. At the same time, the length of AC cannot exceed the length of AB, otherwise the angle B is no longer the inner angle. Therefore, csin45 ° can be obtained

In the triangle ABC, a = x, B = 2, angle B = 45 degrees, if there are two ranges for finding X in this triangle

b/sinB=a/sinA
SO 2 / (√ 2 / 2) = x / Sina
sinA=2√2/x
B=45
So a