Question 884120
the following picture shows the relationship between all the parts.


see below the picture for the analysis.


<img src = "http://theo.x10hosting.com/2014/jun2501.jpg" alt="$$$" </>


tan(30) = a/x


tan(60) = b/x


solve both these equations for x to get:


x = a/tan(30)


x = b/tan(60)


for ease of presentation, let T30 = tan(30) and T60 = tan(60).


because they both equal x, then they are both equal to each other so  you get:


a/T30 = b/T60


multiply both sides of this equation by T30 to get:


a = T30/T60 * b


since a + b = 100, you can solve for b to get b = 100 - a.


substitute for b in the equation of a = T30/T60 * b to get:


a = T30/T60 * (100 - a)


simplify this to get:


a = (T30/T60 * 100) - (T30/T60 * a)


add (T30/T60 * a) to both sides of this equation to get:


a + (T30/T60 * a) = (T30/T60 * 100)


factor out the a on the left side of the equation to get:


a * (1 + T30/T60) = (T30/T60 * 100)


divide both sides of this equation by (1 + T30/T60) to get:


a = (T30/T60 * 100) / (1 + T30/T60)


since T30/T670 = 1/3, you can replace T30/T60 with 1/3 and solve for a to get:


a = (1/3 * 100) / (1 + 1/3) which becomes:


a = (1/3 * 100) / (4/3) which becomes:


a = (1/3) * (3/4) * 100 which becomes:


a = 25


since a + b = 100, this means that b = 75 which means that the height of tower A is equal to 75.