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    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?
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    (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
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    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.
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    (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?
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    (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.
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    Ah got it, so it's 180-110=70

    360-(70+26.5)=263.5

    Cheers.
 
 
 
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