In △ ABC, a = xcm, B = 2cm, B = 45 ° are known. If there are two solutions of triangle by using sine definite, then the value range of X is () A. 2<x<22B. 2<x≤22C. x>2D. x<2
∵ in △ ABC, a = xcm, B = 2cm, B = 45 °, according to the sine theorem Asina = bsinb, Sina = asinbb = x · 222 = 24x, ∵ B = 45 °, 0 < a < 135 °, in order to make the triangle have two solutions, we can get 45 ° < a < 135 °, that is 22 < Sina < 1, ∵ 22 < 24x < 1, the solution is 2 < x < 22, so we choose: a
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- 1. 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
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