trigonometry
posted by nina .
A ship is sighted directly east of a lighthouse. Another ship, which is 20m away from the first ship, is observed at a bearing of N25degreesE from the lighthouse. If the first ship is 4.1 km away from the lighthouse, what is the distance of the second ship from the lighthouse?

angle at ship B
(sin 25)/20 = (sin A)/4.1
sin A = .0866
A = 4.97 deg
angle at ship A
A = 180  25  4.97 = 150.03 degrees
then law of cosines
d^2 = 20^2 + 4.1^2  2(20)(4.1)cosA