hello.

In an orieteering competion a competitor walks for 1.6km on bearing sixty degrees from checkpoint A to checkpoint B. She then alters course to bearing 154 degrees wand walks for a further 2.3km to check point C.
Draw a diagram to show the triangular course.
calculate the distance from check point C to checkpoint A giving your answer to a siutable degree of accuracy.
the answer from checkpoint C to checkpoint A is 2km is this correct?
how do I draw this?

next question
A tanker is moving 5 nautical miles (5 knots) on bearing 105 degrees.at 1100 hours (11am) the tanker obserbs a lighthouse on bearing 040 degrees. at midday the lighthouse bears 340 degrees.
Draw a well labelled diagram to show the movement of the tanker between 11am and midday.
calculate the distance in nautical miles from the tanker to the lighthouse at midday.
thanks.

when calculating these questions what are the difrrences in the real worls and maths world?
I.e the earth is not flat.
what else?

I've attached two sketches.

1. Walking-competition: Calculate the angle , use Cosine rule to calculate the distance AC.

2. Tanker: Calculate the sides of the triangle P1100, P1200, LH using Sine rule. Afterwards calculate the length of the height from LH to the base P1100P1200.

The distance fromm P1100 to the foot point of the height indicates the time from 11:00 o'clock when the lighthouse is nearest to the tanker (11:24 o'clock)

Attached Thumbnails

   

how do I find the cosine rule for the walker? its 360 degrees minus 154 then what is the cosine angle? for the tanker how do I find the sine length?

The angle consists of 2 parts:

- the red part is 60° (alternate angle to the known angle of 60°)

- the orange part: 180° - 154° = 26°

Therefore the complete angle is 60° + 26° = 86°

Attached Thumbnails