First, please allow me to say "Thank you!" for showing your work and reasoning so nicely!

Because they state that the angles are of "depression", not "elevation", I agree with your interpretation of the location of these measured angles.

I agree. However:

Let's use what we know from "real life". If the rope is longer (as LN is longer than LM), then the

angle to get there must be shallower. (A steeper angle of depression would result in the rope reaching the ground faster!) So the listed information cannot be correct; the angle of depression for LM can not be larger than the angle of depression for LN. Or else the ropes' lengths must be different from what is listed.

What happens if we reverse the angle measures?

The angles of depression of *M* and *N* from *L* are 28.7^{o} and 39.5^{o}, respectively.

Then we get:

. . . . .NP/9 = sin(39.5

^{o})

. . . . .NP = 9*sin(39.5

^{o}) = 5.7247...

This doesn't match the book, either. So maybe the angles were correct, but the ropes' lengths were swapped...?

*LM* = 9 and *LN* = 6...

This gives us:

. . . . .NP/6 = sin(28.7

^{o})

. . . . .NP = 6*sin(28.7

^{o}) = 2.8813...

So this doesn't match the book's answer, either.

I can only guess that there is a big typo somewhere....

So maybe the book meant to ask for the length of LP? Or whoever wrote the solutions manual copied down the wrong value? I'd ask the instructor about this. You're probably not the only one who's confused!

## Bookmarks