No idea what the textbook is doing

[phospho]

I mean, I used a similar method as they're using, but I didn't get their answer at all. Where did the x-4 come from? (I used x-6), also, I got d = (6-x)tan50 and d = xtan(3) solving this to get x = 4.04

 

[gneill]

I mean, I used a similar method as they're using, but I didn't get their answer at all. Where did the x-4 come from? (I used x-6), also, I got d = (6-x)tan50 and d = xtan(3) solving this to get x = 4.04

Looks like the book's solution is incorrect on two counts. First, the problem statement has changed at some point to have 6m as the length of the rod, while the solution assumes it's 4m. Second, I don't see how they can use the sine function since the hypotenuse's of the triangles are unknown (and not even labelled). They should use the tan function.