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Use the Cosine Rule to find the distance, :A man left his house jogging at 6 am due north at the speed of 10 kph. At 7:00 he decided to change course and jogged due N68°W at the speed of 15 kph. Find
- his distance from his house at 8:00 am
- the bearing of his house from his position at 8:00 am.
Then use the Sine Rule to find another angle in the triangle, and hence the bearing.
What are these - rocket ships? 200 and 150 kph? Anyway, again you'll have to used the Cosine Rule to find the distance apart of the ships at 3.30 pm. Then use speed = distance / time to find the speed of the second ship. Then use Sine Rule to find another angle and hence the bearing.
- Two ships left a pier at 2:00 pm at the same time. The first ship is due S32°W sailing at the speed of 200 kph, while the other ship headed in the direction S25°E sailing at the speed of 150 kph. At 3:30 pm, the first ship stopped due to engine failure and its captain radioed the second ship for help. At that time instant, the captain of the second ship determined the bearing of the first ship and sailed towards it for help. If the second ship reached the first ship at 6:00 pm, at what speed did the second ship sailed towards the first ship? What was the bearing of the first ship from the second ship at 3:30 pm?
- A man left his house driving a car. He traveled in the direction N32°40’35” for 25 km, then changed course and traveled due west at the same speed for 20 km before stopping to rest. At that time instant, how far is the man from his house? What is his bearing from his house at that instant?
Same again here: Cosine Rule and then Sine Rule
- A ship left a port at 12 noon sailed in the direction S32°15’30” at the speed of 120 kph. At 3:00 pm, the ship changed course and sailed in the direction S54°30’45” at the speed of 150 kph. Find the distance and bearing of the ship from the port at 6:00 pm.
... and again here.
Here are some examples of the Sine Rule and the Cosine Rule if you're not sure how they work.