Originally Posted by

**juangohan9** City X is 85 miles due south of City Y, and City Z is 15 miles due west of City X. What is the bearing of City Z from City Y?

I think it is 270.

Because the way bearings work (I think) is just like angles except they are measured clockwise. So that angle from Y to Z is 270 degreees.

A boat sails for 3 hours at 15 mph in a direction 105°17'. How far south has it sailed?

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The slanted line forms an angle of 105 degrees and 17 minutes. What you seek is length of the vertical line. The the angle between the slanted and the vertical is,

$\displaystyle \theta=104^o 77'-89^o 60'=15^o 17'$

Then,

$\displaystyle \cos 15^o 17' = \frac{x}{\mbox{hypotenuse}}$

But the hypotenuse is the length of the slanted line. Which is 45 miles because the ship is traveling at 15 miles per hour for 3 hours. And $\displaystyle x$ is the length of the vertical line.

Thus,

$\displaystyle x=45 \cos 15^o 17'\approx 43.41$