Posted by **Tim** on Sunday, October 23, 2011 at 11:56pm.

A ship sailing parallel to shore sights a lighthouse at an angle of 12 degrees from its direction of travel. After traveling 5 miles farther, the angle is 22 degrees. At that time, how far is the ship from the lighthouse?

- Calculus -
**Steve**, Monday, October 24, 2011 at 10:41am
Let the lighthouse be h miles from shore. Let x be the distance of the ship from a point on shore closest to the lighthouse.

h/(x+5) = tan 12°

h/x = tan 22°

so, equating h,

(x+5)tan 12° = x tan 22°

.212(x+5) = .404x

1.06 = .282x

x = 3.759 mi

Now, the distance of the ship from the lighthouse, d, can be found by

3.759/d = cos 22°

d = 4.05 mi

## Answer This Question

## Related Questions

- math - the Angle of Elevation From a Ship to the Top of a Lighthouse on the ...
- Maths - A ship is sighted from the top of a lighthouse. The angle of depression ...
- Calculus - The captain of a ship at sea sights a lighthouse which is 260 feet ...
- pre-calculus - a ship passes by buoy b which is known to be 3000 yd from ...
- maths - from the top of a light house the angle of depression of a ship sailing ...
- math - please help!! - A lighthouse bears 40 degrees from a ship. After the ship...
- trig - a ship has maintained a bearing of 47 degrees. ( a bearing is the angle ...
- trig - The captain of a ship at sea sights a lighthouse which is 280 feet tall. ...
- trig - The captain of a ship at sea sights a lighthouse which is 120 feet tall. ...
- math - the angle of elevation from a ship to a 135-foot-tall lighthouse is 2 ...

More Related Questions