Question

Solve for x. Show the equation you used and your work.

Answer 1

More information is needed to answer your question.

The answer provided below is on the assumption that |AD| is an angle bisector of <BAC, by Sine rule


`(sin(\angle BAD))/(24)=(sin(\angle BDA))/(36) \\ \\ \Rightarrowsin(\angle BAD)=(24sin(\angle BDA))/(36)`

Also,

`(sin(\angle CAD))/(18)=(sin(\angle CDA))/(x) \\ \\ \Rightarrowsin(\angle CAD)=(18sin(\angle CDA))/(x)`

But,

`\angle BAD=\angle CAD`

Thus,

`(24sin(\angle BDA))/(36)=(18sin(\angle CDA))/(x) \\ \\ xsin(\angle BDA)=27sin(\angle CDA)`

But,
`\angle BDA\ and\ \angle CDA` are supplementary angles, hence they are equal.

Therefore, x = 27