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C2 ASAP SIne rule help needed with bearings

I have this question that has made this whole week annoying I tried and tried and tried till today I surrender I can't handle this please guys !! help
the picture of this so called sine rule bearing question
C2 sine rule.jpg

please explain a step by step cheers guys :colondollar:

Reply 1

claret_n_blue

You can work out the angles at A and B and this will give you angle at the light house. You know how 2 angles and 1 side which you can then use to work out the distance from A.

Reply 2

hosamthemaster

Original post by claret_n_blue

You can work out the angles at A and B and this will give you angle at the light house. You know how 2 angles and 1 side which you can then use to work out the distance from A.

What are angles A and B ? and how do you calculate it ? It is really frustrating I tried sketching all sorts but I wont get to the right solution Can you please go through this and make it like a worked example

Reply 3

Boucly

Always, always, always draw diagrams.

Find a, b, c, d, e. At this point, you have an angle-length pair: 100 and e. Use sine rule.

Spoiler

Not much to say here. Because.. a picture is worth a thousand words. Use um.. trigonometry.

Reply 4

claret_n_blue

Original post by hosamthemaster

No, I'm not allowed to give you the answer. I can only help you work through it.

Let's first start by working out the angles at A and B.

You're question is on bearing. What you need to remember with bearings is that they start at "north" and work their way around clockwise to give you your angles. You already know this otherwise you wouldn't have drawn the picture correctly.

Let's start with A. A has a bearing of 163. So, from facing north at A, you go around clockwise 163 degrees and you will then be facing the lighthouse, correct?

What you also notice from the picture (for A) is that from the points north to east, there is a right angle (i.e