# Question a375a

Mar 16, 2017

14.43 miles

#### Explanation:

First draw a triangle with two points parallel and vertical with the third point being to the right of the two. The two vertical points are the ship and the third point is the lighthouse.

You can determine that the bottom most point (the ship) has an angle of 25 degrees to the lighthouse.

Then if you were to extend the vertical line upwards past the top point and make an angle from the vertical line (north which is 0 degrees) to the side of the triangle (the angle should be outside of the triangle) it would be 120 degrees. then subtract 120 from 180 to get 60 degrees as the interior angle (this should be the second angle in the triangle). You can do this because the angles are supplementary.

To get the third angle, simply subtract 180 from the sum of the other two angles to get 95 degrees.

Then, since the ship traveled 8.3 mi/h for two hours, it traveled a total of 16.6 miles. You can label the line connecting the two vertical points 16.6 miles.

You can then use the law of sines to figure out the side connecting the bottom ship point to the lighthouse...

$\sin \frac{95}{16.6} = \sin \frac{60}{x}$

x=(16.6sin(60))/(sin(95)#=14.43 miles