Question

A fire at a building B is reported on telephone to two fire stations F1 and F2,10km apart from each other on a straight road. F1 observes the fire at an angle of 60 degree to the road andF2 observes it at at an angle of 30 degree from it. Which station should send it's team and how much will it have to travel?

Answer 1

F1 is nearer to the building
let distance between f1 and B be x
so tan 60 = b/x
√3x=b
now as f2 is 10 km away from f1(given) so
tan 30= b/(10+x)
1/√3(10+x)= √3x
10+x=3x
x=5
so f1 will have to cover 5 km