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?

Answer :


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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