We will use the concept of similar triangles to solve this problem. We will use two triangles: ΔABC and ΔCBD. Next we will establish relations between them. Given that:
BC = m
AC = 18
AD = 11
DC = 7
We will name the some angles as follows:
∠ACB = ∠DCB = β
So the following relations from the triangles are equal to:
(1) [tex]cos( \beta )= \frac{7}{m}[/tex]
(2) [tex]cos( \beta )= \frac{m}{18}[/tex]
So, matching these equations:
[tex] \frac{7}{m}= \frac{m}{18} [/tex]
Solving for m:
[tex]m^{2} = 18x7 = 126[/tex]
∴ [tex] m = \sqrt{126}[/tex]
