trig word problem...totally lost

[iluvblueroses]

Two ships leave a harbor at the same time. One ship travels on a bearing of S 12 degrees W at 14 miles per hour, The other ship travels on a bearing of N 75 degrees E at 10 miles per hour. How far apart will the ships be after three hours? Round to the nearest tenth of a mile.

 

[soroban]

angle, triangle

Hello, iluvblueroses!

Did you make a sketch?

Two ships leave a harbor at the same time.
One ship travels on a bearing of S 12 degrees W at 14 miles per hour,
The other ship travels on a bearing of N 75 degrees E at 10 miles per hour.
How far apart will the ships be after three hours? Round to the nearest tenth of a mile.

*

          N                   o B
          :              * *
          :      30 *   *
          :    *     *
        H o - - - * - - E
         *:    *
     42 * : *
       * *:
    A o   :
          S

$\displaystyle \text{The first ship starts at }H\text{ and sails for 3 hours at 14 mph to }A.$
. . $\displaystyle \angle A\!H\!S = 14^o,\;H\!A = 42\text{ miles.}$

$\displaystyle \text{The second ship starts at }H\text{ and sails for 3 hours at 10 mph to }B.$
. . $\displaystyle \angle B\!H\!N = 75^o,\;\angle B\!H\!E =15^o,\; H\!B = 30\text{ miles.}$

$\displaystyle \text{We have triangle }AHB\text{ with sides }H\!A = 42,\:H\!B = 30,\text{ and included angle }119^o.$

$\displaystyle \text{Law of Cosines: }\:AB^2 \;=\;42^2 + 30^2 - 2(42)(30)\cos119^o$

$\displaystyle Go\:f\!or\;it!$

 

[Nathan13]

How did you get the 119 degree?​

 

[mmm4444bot]

It appears that soroban made a transposition error (i.e., mistakenly swapped value 14 for 12, from the givens).

In other words, angle AHS is 12 degrees.

12 deg + 90 deg + 15 deg = 117 deg

Is this what you were asking about? :cool: