SOLUTION: 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.img

Question 1026017: 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 got all the way to having 2 expressions which equal BC, namely; BC = x/tan55,and BC = x/tan11.2 - 2640, but now I'm confused what to do.
I've spoken to several people, and they've given me different answers. Which is the correct way?
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) -2640
x( 1/ tan(55) - 1/(tan(11.2)) = -2640
x = -2640 / ( 1 /tan(55)) - (1/tan(11.2)) ) = -2640/-4.350161509 = 606.8740194
X = 607 feet
???
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I set it up making y the missing piece of the long leg.
tan 55=x/y
tan 11.2=x/(2640+y)
without rounding, (I will here)
1.428 y=x
522.73+0.1980y=x
Set them equal,
y=425 feet
x=607 feet
a to c is 3065 feet

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