Help idk how to do this problem

Question

CONSTRUCTION An electrician is carrying a ladder horizontally around a corner from one hallway to another. One hallway is a foot wider than the other. If θ = 30°, find the exact length of the ladder.

A )8 + 2 √3

B) 6 √3

C )12

D)(−18 + 8 √3)/3

Answer 1

I do not get any f the possible answers. I will show you my work and you can then judge for yourself.

The ladder touches the inside corner of the hallway and makes a 30° angle with the opposite wall.

Draw a figures Show the ladder as CDE where C, C and E are the points where the ladder touch the walls.

Extend the line of the wider hallway from D to A and draw AB parallel to CE.

There are 3 congruent right triangles: ADE, OBA and DBC where O is the outside cornerof the hallway.

Call x the width of the narrower hall and x+1 the wider width.

From the figure tan 30° = x/(x+1) => (1+√3)/2.

Because these are 30-60 right triangles the hypotenuse is twice the shorter side, and, therefore, again from the figure the ladder is 4x = 2(1+√3).

If you get a different answer in class, I would appreciate your poiting out the flaw in my derivation. Thank you.