Question 1159090
<pre>{{{drawing(200,138,-10,290,-138,69,line(0,0,0,300),
line(0,0,278.7720662,59.25),line(278.7720662,59.25,278.7720662,-128.5890162),
line(0,0,278.7720662,-128.5890162), locate(0,0,A),locate(285,66,B)
red(arc(0,0,100,-100,12,90)),red(locate(3,40,78^o)),locate(285,-122,C),
green(arc(0,0,140,-140,335,450)), blue(line(0,0,278.7720662)),
locate(285,8,D), locate(120,55,285), locate(5,69,E), locate(120,-70,307),
green(locate(55,65,"??"^o))

)}}}

∠BAD = ∠EAD-∠EAB = 90°-78° = 12°

|BD|/|AB| = cos(∠BAD)

|BD| = |AB|∙sin(∠BAD) = 286∙sin(12°) = 59.46274357

|AD|² = |AB|²-|BD|² = 285² - 59.46274357² = 77689.18213

|DC|² = |AC|²-|AD|² = 307²-77689.18213 = 16559.81787

{{{abs(DC) = sqrt(16559.81787) = 128.6849559}}}

sin(∠DAC) = |DC|/|AC| = 128.6849559/307 = 0.4191692375

∠DAC = sin<sup>-1</sup>(0.4191692375) = 24.78214909°

Bearing from A = ∠EAC = ∠EAD+∠DAC = 90°+24.78214909° = 114.7821491°

|BC| = |BD|+|DC| = 59.46274357+128.6849559 = 188.1376995m

Edwin</pre>