A fire in the 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 the fire is at the 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?


Dear Student!

Here is the answer to your query.



Let B be the building and A be the fire.

Given : P and Q are 2 fire stations 20 km apart.


Let the height of AB be h km

and PB = x km. then BQ = (20 – x) km

also ∠APB = 60° and ∠AQB = 45°






equating (1) and (2) we get

⇒PB = 7.32 km and BQ = (20 – 7.32) km = 12.68 km


since PB < BQ i.e.,

Distance from Pl < Distance from Q


∴ P station should send its team to travel 7.32 km.



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