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amirah ,who is at a point P ,observes a boat at pont B 1200m from P in direction 047 degrees. The boat is moving due north of B at a speed of x km/h . fifteen minutes later ,the boat reaches a point C Fifteen minutes later , the boat reaches a point C such as the bearing of C from P is 030 degrees. find value of x

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sqdancefan

Answer:

  about 2.81 km/h

Step-by-step explanation:

It can be useful to draw a diagram.

The lines pointing to due north from points B and P are parallel, so the angle BCP and the bearing of point C from P are the same, 30°. The angle BPC will be the difference of bearings of B and C at P, so is 47-30=17°. This is enough information to solve the triangle using the Law of Sines:

  PB/sin(C) = CB/sin(P)

  CB = PB·sin(P)/sin(C) = (1200 m)·sin(17°)/sin(30°) ≈ 701.7 m

The speed of the boat is then ...

  x = distance/time = (0.7017 km)/(1/4 h) = 2.8068 km/h

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