sin and cosine question

[lovely_nancy]

could you please guide me through this question please:
Im not particularly sure with the sketch and how to go on about it

At midnight, a ship sailing due north passes two lightships, A and B which are 10km apart in line due east from the ship than B. At 2 am the bearing of the lightships are 149degrees and 142degrees.

(i) Draw a sketch to show A and B are and the position of the ship at midnight and 2am
(ii) Find the distance of the ship from A at 12 am.
(iii) Find the speed of the ship

 

[galactus]

If I understand correctly, the picture may help.

Angle ACD is 180-149=31 degrees

Angle ABD is 180-142=38 degrees.

Thus, length DC=x

Length AD is \(\displaystyle x\cdot cot(31)\) as well as \(\displaystyle (10+x)cot(38)\).........[1]

So, length AD can be found by equating and solving for x, which is DC.

\(\displaystyle x\cdot cot(31)=(10+x)cot(38)\)

Solve for x. x is also the value in part ii.

Then, sub that back into either expression in [1] to find AD.

This is the vertical distance from the ship to the light ships.

Divide this value by 2 to find the ships speed in part iii.