Trigonometry help, measuring the earth!?

Posted on 2016-03-02 18:54:00 in Math by KARTIK

Angle 
A= 87.77 degrees 
B=90 
C=2.23 

Side length 
AC= 3 miles + r 
CB=r 
BA=m 

I need to solve for r, I used a method that makes sense to me but doesn't give the correct answer. I want to know why it is wrong. 
sin(2.23)=m/(3+r)=cos(87.77) using co function theorem thus 
3sin(2.23)+rsin(2.23)=m=3cos(87.77)+rco... Implies 
3sin(2.23)+rsin(2.23)=3cos(87.77)+rcos(... using this rule; (a=b=c thus a=c) 
3sin(2.23)+rsin(2.23)=3cos(87.77)+rcos(... 
3sin(2.23)-3cos(87.77)=rcos(87.77)-rsin... 
3sin(2.23)-3cos(87.77)=r(cos(87.77)-sin... 
(3sin(2.23)-3cos(87.77))/(cos(87.77)-si... 
Thus I should have solved r but the value I get is completely wrong. 
r apparently equals -4.8*10^13miles 
I know you can simply take cos(2.23)= r/3+r which implies 
(3cos(2.23))/(1-cos(2.23))=r 
r=3958miles 
I just don't understand why the other approach doesn't work.

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