三、應用題
5.
Suppose the values of \(\alpha\) and \(\beta\) are independently chosen uniformly from the interval \((0,2)\). Provided that the numbers \((1,\alpha,\beta)\) can form the sides of a triangle, find the probability that the numbers form an acute triangle.
在區間(0,1)當中,隨機任選兩個相異點x和y,即可將此區間分成長度各為a,b和c的三個子區間。
已知每一個序對(a,b,c)出現的機率均等,試問a,b和c可以作為一個三角形的三邊長的機率為何?
(100台中區複賽試題二試題,
https://math.pro/db/viewthread.php?tid=1349&page=1#pid7179)
可形成銳角三角形的機率
![](https://math.pro/db/attachment.php?aid=1448&k=3741c44bff1835c0a5435118a2ff784c&t=1685361661&noupdate=yes)