two boats, A and B, left a port C at the same time on different routes. B travelled on a bearing of 150 degree and A travelled on the north side of B. when A had travelled 8 km and B had travelled 10 km , the distance between the two boats was found to be 12 km. show the diagram and calculate the bearing of A`s route from C

Question

two boats, A and B, left a port C at the same time on different routes. B travelled on a bearing of 150 degree and A travelled on the north side of B. when A had travelled 8 km and B had travelled 10 km , the distance between the two boats was found to be 12 km. show the diagram and calculate the bearing of A`s route from C

Answer 1

well, the angle θ between the two boats' headings (not bearings!) can be found via the law of cosines:

12^2 = 8^2+10^2 - 2*8*10 cosθ

Answer 2

To solve this problem, we can start by drawing a diagram to visualize the situation.

Let's label the starting point, or port, as C. Boat A is traveling on the north side of Boat B. We'll represent Boat A's position with the point A, and Boat B's position with the point B.

Since Boat B traveled 10 km and the distance between the two boats is 12 km, we can draw a line segment of length 12 km connecting points A and B.

Next, we'll draw a line extending from point C to point B, representing the route of Boat B. The bearing of Boat B's route is given as 150 degrees.

To calculate the bearing of Boat A's route from point C, we'll use some trigonometry. Since Boat A has traveled 8 km, we can draw a line segment of length 8 km connecting point A to a point D on the line segment connecting points A and B.

Now, we have a right triangle CBD, where angle C is 90 degrees. We want to find the bearing of Boat A's route from point C, so we need to calculate angle CDB.

Using trigonometry, we can use the following formula:

tan(angle CDB) = (BD / CD)

Since BD is the distance between points B and D, which is given as 12 km - 8 km = 4 km, and CD is the distance between points C and D, which is given as 8 km, we can substitute these values in for the formula:

tan(angle CDB) = (4 km / 8 km) = 1/2

Now, we can take the inverse tangent of 1/2 to find angle CDB:

angle CDB = arctan(1/2) = 26.565 degrees

Finally, to find the bearing of Boat A's route from point C, we subtract the angle CDB from 360 degrees (since bearings are measured clockwise from north):

Bearing of A's route from C = 360 degrees - 26.565 degrees = 333.435 degrees

Therefore, the bearing of A's route from C is approximately 333.435 degrees.