How to find the distance with triangles ; Trigonometry

Question

Frank and Marie set sail from the same point. Frank is sailing in the direction S6°E degrees . Marie is sailing in the direction S14°W . After 10 hours, Marie was 10 miles due west of Frank. How far had Marie sailed?Round your answer to four decimal places.°

Answer 1

IF the angles mean what they seem to mean

although 56 east seems to mean S56E

Let x be the distance Marie went horizontally west and 10-x = the distance Frank went horizontally east

then

tan14 = .25 = y/x, tan56 =1.48 = y/(10-x) where y= distance each went south from the start

y = .25x = 1.48(10-x) = 14.8 - 1.48x

1.73x = 14.8

x = 14.8/1.73 = 8.555

Marie's distance from start = 8.555/cos14 = 8.555/.97 = 8.82 miles