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# C2 Bearings Watch

1. While revising for C2 I stumbled upon a question which involves bearings.

Here's the question:

A lifeboat station is at point A. A distress call is received and the lifeboat travels 15km on a bearing of 030° to point B. A second call is received and the lifeboat then travels 27km on a bearing of 110° to arrive at point C. The lifeboat then travels back to the station at A.

(i) Show that angle ABC is 100°

(ii) Find the distance that the lifeboat has to travel to get from C back to A

(iii) Find the bearing on which the lifeboat has to travel to get from C to A.

I proved part one:

360-(150+110)=100

I solved part (ii) with the cos rule and got 33.08 for the angle

I have trouble with point (iii) cause I have no idea how to find out the bearing there.
I found the angle C using the sin rule

sin(100)/33.08=sinC/15

Angle C=26.5 degrees

Now how do I go on from here to find the bearing from C to A?
2. (Original post by Blackfyre)
While revising for C2 I stumbled upon a question which involves bearings.

Here's the question:

A lifeboat station is at point A. A distress call is received and the lifeboat travels 15km on a bearing of 030° to point B. A second call is received and the lifeboat then travels 27km on a bearing of 110° to arrive at point C. The lifeboat then travels back to the station at A.

(i) Show that angle ABC is 100°

(ii) Find the distance that the lifeboat has to travel to get from C back to A

(iii) Find the bearing on which the lifeboat has to travel to get from C to A.

I proved part one:

360-(150+110)=100

I solved part (ii) with the cos rule and got 33.08 for the angle

I have trouble with point (iii) cause I have no idea how to find out the bearing there.
I found the angle C using the sin rule

sin(100)/33.08=sinC/15

Angle C=26.5 degrees

Now how do I go on from here to find the bearing from C to A?
Use your sketch, noting where bearings are measured from
3. Use the sine rule to get angle BCA, and use the rule that interior angles add up to 180 degrees (At B & C).

Now add those 2 values together and take it away from 360 degrees and you'll have the bearing from C to A.
4. (Original post by 0x2a)
Use the sine rule to get angle BCA, and use the rule that interior angles add up to 180 degrees (At B & C).

Now add those 2 values together and take it away from 360 degrees and you'll have the bearing from C to A.
I noted in the thread that I calculated BCA, it's 26.5

How do I use the rule that all angles add up to 180 in this situation?
5. (Original post by Blackfyre)
I noted in the thread that I calculated BCA, it's 26.5

How do I use the rule that all angles add up to 180 in this situation?
The 2 angles between the North-line and line segment B and C are interior angles. You already know the angle between the North-line and point B, so you can work out the one at point C.
6. Ah got it, so it's 180-110=70

360-(70+26.5)=263.5

Cheers.

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Updated: April 9, 2013
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