Q. 40

# A fire in a building B is reported on teleported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. Which station should send its team and how much will this team have to travel?

Let the height of building be 'h'.
Let the distance between P and foot of building is 'x' metres.

In ∆PRS

tan 60° =

√3 =

h = √3x ---------(1)

In ∆QRS

tan 45° =

tan 45° =

1 =

h = 20+ ---------(2)

on substituting the value of h from eqn. (2) in eqn. (1)

20+= √3

√3 = 20

On rationalising above fraction we get,

⇒ 10(√3+1)

x = 10(1.732+1)

Therefore Station P has to send the team. And the distance between station P and the building is 27.32 m.

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