You are on a fishing boat that leaves its pier and heads eas

You are on a fishing boat that leaves its pier and heads east. After traveling for 30 miles there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of S 45° W for 12 miles. At this time, how far are you from the boat\'s pier? Round to the nearest tenth of a mile.

Solution

boat went 30 miles to the east

it turns and head south at 45 degree west for another 12 miles

lets consider a triangle with 1 side 30 mile long with an angle 45° and then 12 miles back

thus, eqn is then the law of cosines

i.e. c^2= a^2+b^2-2ab*cos45

c={30*30+12*12-2*30*12(1/2)

=(543.883)

=23.12