[Math] Bearings Problem

euclidean-geometrytrigonometry

I'm presented with the following bearings problem. I believe I have graphed it correctly, although I don't know where to go from here.

A US Coast Guard patrol boat leaves Port Cleaveland and averaged 35
knots (nautical mph) traveling for 2 hours on a course of 53 degrees
and then 3 hours on a course of 143 degrees.

enter image description here

I need to find the boat's bearing and distance from Port Cleaveland.

Best Answer

Won't you calculate the degrees from the east direction?. If you did, it is simple application of pythogorus theorem. It travels 2*35 nm at 53 degress to the east. Then it travels 3*35 nm at 143 degrees to the east. It's position is $\sqrt{70^2 + 105^2} = 126.2$ miles from the port of cleaveland and it is 109.3 degrees to the east.

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