Question #e38b9

1 Answer
Sep 29, 2015

Always sketch and label the angles and distances on paper so that it will be easier to see the problem.

Explanation:

Here is a sketch of the problem:

enter image source here

Using the properties of parallel lines and transversals, it is true that angle ABC is a right angle .

Since we know the lengths of the sides of the right triangle, it now easy to use the Pythagorean Theorem to to find the distance from A to C:

#81^2 + 74^2 = (bar(AC))^2#
#bar(AC) = 109.71# miles

#/_C# can be found using the inverse tangent:

#Tan C# = #81/74#

#C=47.6^o#

Again, using parallel lines and transversals, you can determine from point C that the angle between South and point A is 47.6+25 = 72.6 degrees.

The bearing from C to A will be #S(47.6^0+25^0)#W = #S72.6^0W#

Hope that helped