Question

PLEASE PLEASE HELP ASAP

Answer 1

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) $cos( \beta )= \frac{7}{m}$
(2) $cos( \beta )= \frac{m}{18}$

So, matching these equations:

$\frac{7}{m}= \frac{m}{18}$

Solving for m:

$m^{2} = 18x7 = 126$
∴ $m = \sqrt{126}$