Posted by **Amber** on Saturday, June 23, 2012 at 10:31am.

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 :)

- Trigonometry -
**bobpursley**, Saturday, June 23, 2012 at 10:54am
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(90-52)=d/sin90

so you know then d=originaldistance/sin38 at 5PM

also, from the law of cosines..

originaldistance^2=d^2+(15t)^2-2d15tcos38 where t=2

now, you can solve for all.

- Trigonometry -
**irish**, Thursday, November 21, 2013 at 6:10am
24.36

## Answer This Question

## Related Questions

- Trigonometry - A person on a ship sailing due south at the rate of 15 miles an ...
- Algebra - Sorry for asking another question, but I don't know how to set this ...
- Algebra 3 and trig - An ocean liner is 177 miles due west of lighthouse A. ...
- trigonometry - At a certain time, a lighthouse is south of a ship. Thirty ...
- calculus - Optimization At 1:00 PM ship A is 30 miles due south of ship B and is...
- Calculus - One ship is 20 miles due North of another ship, and is sailing South ...
- Mathamatics - A ship is due south of a lighthouse. It sails on a bearing of 72* ...
- Math 12A Plain Trigonometry - a boat leaves lighthouse P and sails 10 miles. At ...
- CALCULUS!!!!! - At 9am, ship B was 65 miles due east of another ship, A. Ship B ...
- calculus - At 9am, ship B was 65 miles due east of another ship, A. Ship B was ...

More Related Questions