Trigonometry and Bearings

[dinosaur93]

A lifeguard observes a rescue boat due north of his position on the beach. The lifeguard also observes a distress swimmer on a bearing of N 52⁰E at a distance of 470m. The swimmer is due east of the rescue boat. Unfortunately, the rescue boat is experiencing difficulties and is unable to reach the swimmer. The lifeguard looks a further 25⁰ to the right of the swimmer in distress and spot a shark 900m away.

Question
What is the distance between the swimmer and the shark? Who is closer to the swimmer, the shark or the rescue boat?



In order for the lifeguard to rescue the distress swimmer, the shark needs to be caught. A second rescue boat on the beach due east of the lifeguard is equipped to catch the sharks. The second rescue boat is in a direct line with the shark and the swimmer.


How do you draw the diagram representing in red?


Question
Calculate how far the boat must travel and on what bearing to catch the shark, given the shark has not begun to approach the swimmer yet.

[seretide]

Sorry but "A lifeguard observes a rescue boat due north of his position on the beach. " How is that possible if north is shown in the opposite direction?Or have you mistyped? Or have I lost the plot...

[dinosaur93]

oh yeah, the directions of the diagram is wrong, it should be the other side, Im terribly sorry!

[dinosaur93]

could anyone pls help me draw this diagram?

[dinosaur93]

anyone?

[smithy16]

The bearing they must travel on is 103 degrees, and the distance is already stated - 900m

[dinosaur93]

cheers!