app of trigonometry

[sowmya]

hey friends.....pls answer....

A fire in a building B is reported on telephone to two fire stations P and Q , 20km apart from each other on a straight road.P observes that d fire s at an angle of 60^ to the road and Q observes that it s at an angle of 45^ to d roads.which station should send it's team and hw much will this team hav to travel??

[Nanooji]

consider the building to b AB and fire is at B
On either sid of this building r the two fire stations P and Q
Let the angle of elevation of P be 60 degree (to B)
Let the angle of elevation of Q be 45 degree (to B )
The distance between P and Q is 20 km and A , the base of the building is in path of P and Q
Let the distance between P and A be 'x'
Let trhe distance between A and Q be '20-x'
Let the height of the building be 'h'


Therefore from triangle BAP
tan 60=h/x
root 3=h/x
x root 3 = h ------------------> eq 1



From triangle BAQ

tan 45 = h/20-x

1 = h/20-x

20-x = h -----------------------> eq 2




from 1 and 2 eq

20 -x = x root 3

20 = x root 3 + x
20 = x (root 3 + 1)
20/root 3 + 1 = x

on rationalising with root 3 - 1
10 (root 3 - 1) = x
therefore x = 7.32 km



thus the distance between A and P is 7.32 km
and between A and Q is 12.7 km

[sowmya]

thanks.