(a) First, we need to calculate how far each ship has traveled.

Ship A has been traveling for 3 hours at a speed of 25km/h, so it has traveled 3*25 = 75km.

Ship B has been traveling for 3 hours at a speed of 20km/h, so it has traveled 3*20 = 60km.

Now, we need to calculate the distance between the two ships. We can use the law of cosines for this. The law of cosines is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

In this case, the angle between the paths of the two ships is 152° - 80° = 72°.

So, the distance between the two ships is sqrt(75^2 + 60^2 - 2*75*60*cos(72°)) = 70.71km (rounded to 2 decimal places).

(b) To find the bearing of B from A, we need to use the law of sines. The law of sines is a formula that relates the lengths of the sides of a triangle to the sines of its angles.

First, we find the angle opposite to the side representing the distance from A to B.

sin(angle) = 60*sin(72°) / 70.71. Solving for angle gives us angle = arcsin(60*sin(72°) / 70.71) = 59.04°.

The bearing of B from A is then 80° + 59.04° = 139.04° (rounded to 2 decimal places).

Question

(a) First, we need to calculate how far each ship has traveled.

Ship A has been traveling for 3 hours at a speed of 25km/h, so it has traveled 3*25 = 75km.

Ship B has been traveling for 3 hours at a speed of 20km/h, so it has traveled 3*20 = 60km.

Now, we need to calculate the distance between the two ships. We can use the law of cosines for this. The law of cosines is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

In this case, the angle between the paths of the two ships is 152° - 80° = 72°.

So, the distance between the two ships is sqrt(75^2 + 60^2 - 2*75*60*cos(72°)) = 70.71km (rounded to 2 decimal places).

(b) To find the bearing of B from A, we need to use the law of sines. The law of sines is a formula that relates the lengths of the sides of a triangle to the sines of its angles.

First, we find the angle opposite to the side representing the distance from A to B.

sin(angle) = 60*sin(72°) / 70.71. Solving for angle gives us angle = arcsin(60*sin(72°) / 70.71) = 59.04°.

The bearing of B from A is then 80° + 59.04° = 139.04° (rounded to 2 decimal places).

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