A Coast guard cutter detects an unidentified ship at a distance of 18.6 km, the

Question

A Coast guard cutter detects an unidentified ship at a distance of 18.6 km, the direction 14.7 Degree east of north. The ship is travelling at 28.6 km/h on a course at 35.3 Degree east of north. The coast guard wishes to send a speedboat to intercept the vessel and investigate the vessel. If the speedboat travels 51.3 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north? Your response differs from the correct answer by more than 10%. Double check your calculations. Degree east of north

Explanation / Answer

here

the angle between the two vectors = 180 + 14.7 - 35.3 = 159.4 deg

then by using law of sines

sin(theta) / 28.6 *t = sin(159.4) / 51.3*t

sin(theta) = sin159.4 * 28.6 / 51.3

theta = sin^-1(0.1962)

theta = 11.31 deg east of north

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