SOLUTION: ship A is due west of a lighthouse. ship B is 12 km southof ship A. from ship B, the bearing to the lighthouse is N63°20'E, how far is ship A from the lighthouse? answer

Algebra ->  Trigonometry-basics -> SOLUTION: ship A is due west of a lighthouse. ship B is 12 km southof ship A. from ship B, the bearing to the lighthouse is N63°20'E, how far is ship A from the lighthouse? answer      Log On


   

Question 1107725: ship A is due west of a lighthouse. ship B is 12 km southof ship A. from ship B, the bearing to the lighthouse is N63°20'E, how far is ship A from the lighthouse? answer
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the lighthouse and ship A and ship B make a right triangle as shown below:

that triangle is labeled ABC, where C is the position of the lighthouse.

from ship B, the bearing to the lighthouse is north 63 degrees 20 minutes east.

63 degrees 20 minutes is equal to 63 and 1/3 degrees because 20 seconds / 60 = 1/3 minutes.

that angle is shown in the following diagram.

$$$

tangent of 63 and 1/3 degrees is equal to opposite side divided by adjacent side.

that makes tangent of 63 and 1/3 degrees = x / 12.

multiply both sides of this equation by 12 to get 12 * tan(63 and 1/3) = x

solve for x to get x = 23.89396451

here's a reference on bearing you might find helpful.

http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm

your north line in the diagram is represented by the line segment AB.