Radar stations A and B are on an east-west line, 3.7 miles apart.Station A detects a plane at C, on a bearing of 610. Station Bdetects the plane at a bearing of 3210. Find the distance from A to C.
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see diagram.
In the triangle ABC, we have the angle A = 90°-61° = 29°
and angle B = 321° - 270° = 51°
Hence angle C = 100°
Sin A / BC = Sin B / AC = Sin C / AB
AC = AB Sin B / Sin C = 3.7 * Sin 51° / Sin 100° = 2.92 miles
In the triangle ABC, we have the angle A = 90°-61° = 29°
and angle B = 321° - 270° = 51°
Hence angle C = 100°
Sin A / BC = Sin B / AC = Sin C / AB
AC = AB Sin B / Sin C = 3.7 * Sin 51° / Sin 100° = 2.92 miles
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