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?
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.