Question
Island A is 190 miles from Island B. A ship travels 270 miles from Island A, but is off course 180 miles from Island B. What angle, in degrees must the ship turn in order to head straight for Island B?
Answers
Draw a diagram.
Consider A to be at (0,0)
B lies on the circle with center at (0,0) and radius 190
The ship ended up at a point P on a circle with center at (0,0) and radius 270, such that BP = 180
If we let B be due north of A, then the bearing of P from B is z degrees, where
cosz = 80/180
Now you can find the angle θ that the ship is off via
tanθ = 180sinz/270 = 2/3 sinz
Consider A to be at (0,0)
B lies on the circle with center at (0,0) and radius 190
The ship ended up at a point P on a circle with center at (0,0) and radius 270, such that BP = 180
If we let B be due north of A, then the bearing of P from B is z degrees, where
cosz = 80/180
Now you can find the angle θ that the ship is off via
tanθ = 180sinz/270 = 2/3 sinz
Related Questions
A cruise ship sets a course N50°E from an island to a port on the mainland, which is c = 170 miles a...
Ship A is moving east at 20 miles per hour, while ship B is moving north at 15 miles per hour. At no...
Passage #1: Easter Island
Easter Island, also known as Rapa Nui, is an isolated island in the middl...
1%0D%0A%0D%0AEaster Island, also known as Rapa Nui, is an isolated island in the middle of the Pacif...