I have tried everything I can think of on this and I must be missing something. I had a student come into the tutoring center with this. The answer is supposed to be 57.1 degrees. It seems like it should be simple, but I can't for the life of me get 57.1 degrees. So either the book is wrong or, like I said, I am missing something. Which is more likely.
I never thought of that set up. I am starting to think that the book is wrong. The thing is, this question is from a math 53 class, which is a really quick, down and dirty, trig class for building inspection majors. This student only knows basic Sin, Cos, Tan, functions and some area formulas. I don't think that they have ever talked about a line being tangent. Bar that however, I still think the book might have a typo because I have tried everything with every assumption I could think of.
Thank you so much for your help. That was a much better set up than any I had tried
If you come up with anything else please let me know.
It is very early in the morning here and so it could happen that I missed something:
The two right triangles must be congruent: Both have the same hypotenuse and both have a leg of 180. Therefore .
Therefore the angle in question is
It seems to me that I'll reach the correct answer in the next attempt.
I played a little bit with your sketch:
If you cut off 40' from the distance of 365' (which is the wrong method because the width of the road is measured perpendicular from side to side) then you'll get an angle of 57.96°.
Actually you must use the angle to calculate the distance to be cut off the 365' (=44.6') but I don't have the time to do the calculations in detail: I must fetch some rolls for breakfast now.