Question 321320
What we do is run what is known as a 'traverse' around to the second house and 

calculate the distance back to the volcano. Let the volcano have coordinates at the origin (0,0).

Coordinates of house A:

x=15cos(230)=-9.64
y=15sin(230)=-11.49

Now, find the coordinates from house A to house B:

S40E is 140 degrees as an azimuth. An azimuth is an angle turned clockwise from north, or the y axis. 

x=-9.64+14cos(140)=-20.36
y=-11.49+14sin(140)=-2.49

Now, use Pythagoras using these coordinates back to the volcano. 

{{{sqrt((-20.36-0)^2+(-2.49-0)^2)=20.51}}}

They do not need to evacuate. They have 1/2 a mile to spare. Though, that is a close call for a volcano with a pyroclastic flow.:):)