SOLUTION: While An is walking on a straight road running east-west from A to B. which are 10km apart, she sees a church in the distance. The bearing from A to the church is N48E and from B t

Algebra ->  Trigonometry-basics -> SOLUTION: While An is walking on a straight road running east-west from A to B. which are 10km apart, she sees a church in the distance. The bearing from A to the church is N48E and from B t      Log On


   

Question 844938: While An is walking on a straight road running east-west from A to B. which are 10km apart, she sees a church in the distance. The bearing from A to the church is N48E and from B the church is at a bearing of N67W. Find the distance from A to the church.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the only way i could solve this was through the use of the law of sines.
the attached diagram shows you the situation.
$$$
i had to assume she was walking from west to east.
otherwise the church would not have been able to be located.
i translated N48E and N67W based on the information supplied in the following link:
http://www.co.ottertail.mn.us/gis/degrees.php
RT4DP means rounded to 4 decimal places.
i'm assuming this is a trigonometry problem.
i couldn't figure out how to solve it without using trigonometry.
i did verify that the answer is correct by using the law of cosines to solve for the distance after all sides were measured using the law of sines.
The law of cosines confirmed that the length of line segment b was done correctly.