Question 1157899
{{{drawing(2800/13,400,-5,30,-45,20,
arc(0,0,17,-17,30,90), arc(25.98076211,15,17,-17,210,270),
line(0,-50,0,28), locate(.6,7,60^o),
locate(21.4,13,60^o), locate(27,-11,x),
line(0,0,25.98076211,15),locate(11,10,30),locate(9,-20,50),
locate(-1.9,.68,A),locate(26,17.5,B), locate(26,-42.5,C),
line(25.98076211,15,25.98076211,-42.42991873), 
line(0,0,25.98076211,-42.42991873) )}}}

The jet flies from A to B, and AB=30 km. Then from B to C, which is x km,
and AC = 50 km.

We use the law of cosines.  We could have used the law of sines. Maybe
that would have been easier.  

{{{matrix(14,3,
AC^2,""="",AB^2+BC^2-2*AB*BC*cos(B),
50^2,""="",30^2+x^2-2*30*x*cos(60^o),
2500,""="",900+x^2-60*x*(1/2),
2500,""="",900+x^2-30x,
0,""="",x^2-30x-1600,
x,""="",(-(-30) +- sqrt((-30)^2-4*(1)*(-1600) ))/(2(1)),
x,""="",(30 +- sqrt(900+6400) )/2 , 
x,""="",(30 +- sqrt(7300) )/2 ,
x,""="",(30 +- sqrt(100*73) )/2,
x,""="",(30 +- 10sqrt(73) )/2,
x,""="",30/2 +- expr(10/2)sqrt(73),
x,""="",15 +- 5sqrt(73),
positive,value,"",
x,""="",57.72km)}}}

Edwin</pre>