How Far and in What Direction is the First Boat from You After Engine Failure?

[possum30540]

Homework Statement

A boat leaves San Pedro and travels 35 km 15* west of south before its engine dies. You left San Pedro earlier in the morning and have traveled 42 km 23* south of west by the time the first boat's distress all reaches you. How far from and in what direction is the first boat relative to you at that point?

Homework Equations

for the other boat:
bx=-35sin15
by=-35cos15
bz=0

for your boat:
bx=-42cos23
by=-42sin23
bz=0

your boat components - other boat components = direction

magnitude (your boat-other boat)= distance away

The Attempt at a Solution

Direction=[-30, 18, 0] (what directions is this . .)

distance=42

 

[LowlyPion]

Homework Statement

A boat leaves San Pedro and travels 35 km 15* west of south before its engine dies. You left San Pedro earlier in the morning and have traveled 42 km 23* south of west by the time the first boat's distress all reaches you. How far from and in what direction is the first boat relative to you at that point?

Homework Equations

for the other boat:
bx=-35sin15
by=-35cos15
bz=0

for your boat:
bx=-42cos23
by=-42sin23
bz=0

your boat components - other boat components = direction

magnitude (your boat-other boat)= distance away

The Attempt at a Solution

Direction=[-30, 18, 0] (what directions is this . .)

distance=42

The direction you have looks like its from the distressed boat to you. Your vector to the distressed boat looks to me like it should be tan^-1(18/30) degrees south of East.