a man travels from a village A on a bearing of 060 degrees to a village B which is 30km away. From B, he travels to another village C, on a bearing of 195 degrees. If C is directly east of A, calculate, correct to three significant figures, the distance of ; (a) B from C (b) C from A.

Draw the diagram.

Find CA using the law of cosines.
then find CB using the law of sines.

Did you know?

Did you know that bearings are a useful way to describe the direction of travel? In this scenario, a man is traveling from village A to village B on a bearing of 060 degrees, which means he is traveling slightly east of north. The distance between A and B is 30km. From B, he then takes a bearing of 195 degrees, which means he is traveling south of west, to reach village C. Interestingly, if C is directly east of A, we can calculate the distances between all three villages. The distance from B to C is calculated by subtracting 180 degrees from the bearing of 195 degrees, which gives us a bearing of 015 degrees, meaning C is slightly north of east from B. The distance between B and C can then be calculated using trigonometry. Similarly, the distance from C to A can be calculated by subtracting 180 degrees from the bearing of 195 degrees, resulting in a bearing of 015 degrees, indicating that A is slightly north of west from C. Again, we can use trigonometry to calculate the distance between C and A. By using these calculations and rounding to three significant figures, it is possible to determine the precise distances between the villages.