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?

Question

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&#xB0; to the road and Q observes that it is at an angle of 45&#xB0; to the road. Which station should send its team and how much will this team have to travel?

Philoid · Accepted Answer

Let the distance between P and foot of building is ()

In ∆PRS

tan 60° =

√3 =

h = √3 ---------(1)

In ∆QRS

tan 45° =

1 =

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

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

20+= √3

√3 – = 20

On rationalsing above fraction we get,

⇒ ⇒ 10(√3+1)

= 10(1.732+1)

Therefore Station P has to send team. And distance between station P and

Building is 27.32 m.