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 )= (7)/(m)`
(2)
`cos( \beta )= (m)/(18)`

So, matching these equations:


`(7)/(m)= (m)/(18)`

Solving for m:


`m^(2) = 18x7 = 126`
∴
`m = √(126)`