Question

A fire in a building B is reported on telephone to two fire stations P and Q, 20km apart from other on a straight road. P observes that the fire is at an angle of ${60}^{\circ }$ to the road and Q observes that it is at an angle of ${45}^{\circ }$ to the road.
(a) Which station should send its team and how much will this team have to travel?
(b) What according to you, are the values displayed by the teams at fire stations P and Q?

Answer 1

Distance from p = 20-x = 7.32
Distance from Q = x = 12.68
$\therefore$ P is closer to the fire
$\therefore$ Fire station P should be sent and it will have to
$tan\left({45}^{\circ }\right)=\frac{y}{x}=1$
$y=x$
$tan60)=\frac{y}{20-x}=\sqrt{3}$
$\therefore (20-x)\sqrt{3}=y$
$20-\sqrt{3}-\sqrt{3}x=x[\therefore y=x]$
$20\sqrt{3}=(\sqrt{3}+1)x$
$\therefore x=\frac{20\sqrt{3}}{\sqrt{3}}=12.68$
$x=12.68$
$20-x=7.32$