Trigonometry
posted by Amber .
A person on a ship sailing due south at the rate of 15 miles an hour observes a lighthouse due west at 3p.m. At 5p.m. the lighthouse is 52degrees west of north. How far from the lighthouse was the ship at a)3p.m.? b)5p.m.? c)4p.m.?
Please Show The Solution So That I Can Study the Problem. Thanks In Advance :)

draw the picture as a at 3pm and at 5 pm. Label the distance the ship from the ship to the lighthouse as d.
Note d^2=original distance^2+(15t)^2
where t=0 at 3pm, t=2 at 5pm, etc.
Now, at t=2, using law of sines...
original distance/sin(9052)=d/sin90
so you know then d=originaldistance/sin38 at 5PM
also, from the law of cosines..
originaldistance^2=d^2+(15t)^22d15tcos38 where t=2
now, you can solve for all. 
24.36
Respond to this Question
Similar Questions

Algebra
Sorry for asking another question, but I don't know how to set this problem up. Ship A is due west of a lighthouse. Ship B is 12 km south of ship A. From ship B the bearing to the lighthouse is N63E. How far is ship A from the lighthouse? 
Mathamatics
A ship is due south of a lighthouse. It sails on a bearing of 72* for 34 km when it is then due east of the lighthouse. Choose the one option which is closest to the distance (in km) of the ship from the lighthouse when it lies due … 
trig
A boat is 23 mi due west of lighthouse A. Lighthouse B is 14 mi due north of lighthousenA. Find the bearing of lighthouse B from the boat and the distance from lighthousenB tho the boat. 
maths
A ship sailing on a course bearing 036 degrees is 5500 metres due south of a lighthouse.If the ship continues on this course,what is the closest distance the ship will come to the lighthouse? 
Algebra 3 and trig
An ocean liner is 177 miles due west of lighthouse A. Lighthouse B is 265 miles due south of lighthouse A. Find the distance from lighthouse B to the liner and the bearing of the ocean liner from lighthouse B. 
Trigonometry
A person on a ship sailing due south at the rate of 15 miles an hour observes a lighthouse due west at 3p.m. At 5p.m. the lighthouse is 52degrees west of north. How far from the lighthouse was the ship at a)3p.m.? 
trigonometry
The bearing of the lighthouse is N 68 degress E from a ship 43 miles from the lighthouse. How far north of the ship is the lighthouse? 
Math 12A Plain Trigonometry
a boat leaves lighthouse P and sails 10 miles. At the same time, it is sighted from lighthouse Q, 13 miles west of P. The bearing of the ship from Q is North 70 degree and 30 minutes East. Find the distance of the ship from Q. 
trigonometry
At a certain time, a lighthouse is south of a ship. Thirty minutes later, the ship bears N40°20'E from the lighthouse. If the ship is sailing east at 20 kilometers per hour,find the distance of the ship from the lighthouse at each … 
Math
A ship is sailing due north. At a certain point the bearing of a lighthouse is N 40∘E and the distance is 15.5. After a while, the captain notices that the bearing of the lighthouse is now S 54.9∘E. How far did the ship travel …