In how many ways can you select three different numbers from the set [1,2,3,4,5,6,7,8] so that the numbers could represent the measures of the sides of the triangle? The sum of the measures of any two sides must be greater then the measure of the other side.

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft