maths
posted by christine on .
Starting from one oasis, a camel walks 25km in a direction 30 degrees south of west and then walks 30km toward the north to a second oasis. What distance separates the two oases?

I made a quick sketch and found the angle between the two paths to be 60°
So it becomes a simple Cosine Law
x^2 = 25^2 + 30^2  2(25)(30)cos60
= 775
x = √775 = 27.84 appr. 
Take x as east, and y as north, and the starting position as (0,0).
The coordinates of the first stop are
(25cos(30°), 25sin(30°)
The second stop is simply 30km towards +y, or
(25cos(30°), 3025sin(30°)
=(21.65,17.5)
Use Pythagoras theorem to calculate the distance from the original point (0,0).