Values to find: x,y,BC (see picture).
1) Obviously x+y=80°. Via Sinus Theorem
AB=sin(104°)ACsin(36°) & AD=sin(37°+y)ACsin(53°) & AB=sin(60°)ADsin(y) =>
sin(37°+y)sin(60°)ACsin(53°)sin(y)=sin(104°)ACsin(36°)
Using sin(53°)=sin(90°−37°)=cos(37°) we can rewrite previous equation as
sin(37°)cos(y)+cos(37°)sin(y)cos(37°)sin(y)=sin(104°)sin(60°)sin(36°) =>
sin(60°)sin(36°)sin(104°)=1+tg(37°)ctg(y) =>
y=arctg[tg(37°)1(sin(60°)sin(36°)sin(104°)−1)]
y≈arctg(1,19)≈40°
x=80°−y≈40°
2) Via Sinus Theorem AB=sin(40°)BCsin(36°) & AB=sin(60°)ADsin(y) =>
BC=sin(60°)sin(36°)ADsin(y)sin(40°)
BC≈1000m∗0,798=798m
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