Need help solving this

Question

Given the numbers in the linked image, how do I find the following;

A) The value of X to the nearest foot?

B) The distance from A to C to the nearest foot?

http://i.imgur.com/vhOCpbN.jpg

 

I was able to get to the point where I got BC = x/tan55, and BC = (x/tan11.2) - 2640, however I am a bit confused what to do next. I asked several people, and they told me different things. 

 

These are the two solutions I was given (not sure which one to believe);

 

1. [x / tan(11.2)] - 2640 = x / tan(55)
[x / tan(11.2)] + [x / tan(55)] = 2640
x( [1 / tan(11.2)] + [1 / tan(55)] ) = 2640
x(5.75) = 2640
x = 2640 / 5.75
x = 459 ft. 

 

 

2.(x/tan(55)) = (x/tan(11.2) -2460
x( 1/ tan(55) - 1/(tan(11.2)) = -2460
x = -2460 / ( 1 /tan(55)) - (1/tan(11.2)) ) = -2460/-4.350161509 = 565.4962453

 

 

Answer 1

desmos.com/calculator/vijbfimvqe