2. 职称英语
  3. [img]2014m9x/ct_egreqm_egreqbj_0083_20148[/img] [br] BIn this question, you are

[img]2014m9x/ct_egreqm_egreqbj_0083_20148[/img] [br] BIn this question, you are

游客2025-02-24  13
问题 [br]
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答案 B
解析 In this question, you are asked to compare the length of line segment AC with 3.
    Note that in the figure, the vertical line segment divides triangle ABC into two right triangles. Based on the fact that the sum of the measures of the angles in a triangle is 180°, you can conclude that the triangle to the left of the vertical line is a 45°-45°-90° right triangle and the triangle to the right of the vertical line is a 30°-60°-90° right triangle. The following figure shows all of these angle measures, along with a new label D at the vertex of the right angles.

Note that the length of AC is equal to the length of AD plus the length of DC. Also note that AD is a leg of the 45°-45°-90° triangle and DC is a leg of the 30°-60°-90° triangle.
    In the figure, you are given that the length of BC, the hypotenuse of the 30°-60°-90° triangle, is 2. No other lengths are given. Recall that if the length of the hypotenuse of a 30°-60°-90° triangle is 2, then the length of the sideopposite the 30° angle is 1, and the length of the side opposite the 60° angle is. So, in the 30°-60°-90° triangle BDC, the length of DC(the side opposite the 30° angle)is 1, and the length of BD(the side opposite the 60° angle)is.
    Now consider the 45°-45°-90° triangle ABD. Since this is an isosceles right triangle, its legs, AD and BD, have equal length. Since the length of BD is, the length of AD is also.
    As noted above, the length of AC is equal to the length of AD plus the length of DC. Since the length of AD isand the length of DC is 1, it follows that the length of AC is equal to+ 1.
    Recall that in the question you were asked to compare the length of AC with 3. Becauseis less than 2, it follows that the length of AC, which is equal to+ 1, is less than 2 + 1, or 3. Hence, Quantity B is greater than Quantity A, and the correct answer is Choice B.
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