標題:

Probability

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ABCD is a unit square. M is the mid-point of AD.P is a point randomly chosen inside the square. 圖片參考:http://imgcld.yimg.com/8/n/HA00386248/o/701012210264313873429970.jpg a) what is the probability that ∠PMA is an obtuse angle?B) what is the probability that ∠PMA ≦45?C) what is the probability that 70? ≦ ∠PMA... 顯示更多 ABCD is a unit square. M is the mid-point of AD.P is a point randomly chosen inside the square. 圖片參考:http://imgcld.yimg.com/8/n/HA00386248/o/701012210264313873429970.jpg a) what is the probability that ∠PMA is an obtuse angle? B) what is the probability that ∠PMA ≦45? C) what is the probability that 70? ≦ ∠PMA ≦ 110?

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最佳解答:

a) P(∠PMA obtuse) =P(∠PMA >90) =1/2 b)P(∠PMA <=45) =P(P is in triangle AMN), N is the mid point of AB =1/8 c)P(∠PMA between 70 and 110) =P(P is in the isoceles triangle with base BC with vertex M and ∠M=40 ) =area of the isoceles triangle/area of square =[(1/2)(2tan20)(1)]/1 =tan20 =0.364

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