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

Question

3 years ago

8

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

Mathematics

1 answer:

Luda [366] · Answer 1 · 2022-01-06T08:33:17+03:00

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