two boats A and B left a port C at the same time on different routes. B travelled on a bearing of

150 and A travelled on the north side of B. When A had travelled 8km and the two boats was found to be 12km. Calculate the bearing of A route from C. Show your workings and diagram

the speed of the boats is not mentioned...it is a factor

From the question, the three given sides forms a triangle say ABC. By using The Cosine Rule, the angle opposite AB can be found. This angle is 82.8 (to 3 sig. fig.). Therefore,the bearing of A's route from C is 150 - 82.8 = 67.2 degrees.

To calculate the bearing of boat A's route from point C, we need to use trigonometry and draw a diagram. Let's break down the problem into steps:

1. Draw a diagram: Draw point C as the starting point, then draw boat B's route at a bearing of 150 degrees. Next, draw boat A's route on the north side of boat B. Label the distance between boat A and boat B as 12 km and the distance traveled by boat A as 8 km.

2. Determine the triangle: From the diagram, we can see that we have a triangle formed by points C, A, and the current location of boat B. We need to find an angle within this triangle to determine the bearing of boat A's route from point C.

3. Calculate the side lengths: Using the given distances, we know that the distance between A and B is 12 km, and boat A has traveled 8 km. This means that the remaining distance from boat B to point C is 4 km (12 km - 8 km).

4. Use trigonometry to calculate the angle: We can use the tangent function to find the angle. In this case, we know the opposite side (4 km) and the adjacent side (8 km) to the angle we want to find. Let's call this angle θ.

tan(θ) = opposite/adjacent
tan(θ) = 4/8
θ = arctan(4/8)

5. Convert the angle from radians to degrees: The inverse tangent function gives the angle in radians, so we need to convert it to degrees.
θ (in degrees) = arctan(4/8) * (180/π)

Calculating this, we find that θ is approximately 26.57 degrees.

6. Determine the bearing of A's route: The bearing is measured clockwise from the north direction. Since point C is a starting point and boat A traveled on the north side of boat B, the bearing of boat A's route from C is the bearing of boat B's route (150 degrees) plus the angle θ.

Bearing of A's route from C = 150 degrees + 26.57 degrees

Thus, the bearing of boat A's route from point C is approximately 176.57 degrees.

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