A ship leaves port on a bearing of 22° NE and travels 18.5 miles. The ship then turns due east for another 6 miles. How far is the ship from port?

Question

1942 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-14T12:57:14

#29.3# miles to the nearest 1 decimal place.

Let the port be#(A)#
Let the first turning point be #(B)#
Let the 2nd turning point be #(C)#

Bearing from port#(A)=22^@NE=18.5# miles turning point# (B)#

Bearing from turning point #(B)# to port# (A)=22^@+180^@=202^@#

Bearing due East#=90^@#(B)to(C) #=6# miles

#angle at( B)=202^@-90^@=112^@#

In#triangleA,B,C angle B=112^@#

Cosine rule:- #b^2=a^2+c^2-2ac CosB#

#:.b^2=6^2+18.5^2-2*6*18.5*Cos 112^@#

#:.b^2=36+742.25-(2*6*18.5*-0.374606593)#

#:.b^2=778.25-(-83.16266374)#

#:.b^2=861.4126636#

#:.sqrt(b^2)=sqrt(861.412663)#

#:.b=29.34983243#

#:.b=29.3# miles back to port.(A) to the nearest 1 decimal place.