Question

a fire in a building B is reported on telephone to two fire station P and Q, 20 km apart from each other on a straight road P observes that the fireis at an angle of 60 degree to the road and Q observed that it is at an angle of 45 degree to the road. Which station should it send it team and how much will that team have to travel ?

Answer 1

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Answer 2

Answer:

7.320 km

Step-by-step explanation:

Refer the attached figure

AB is the height of Building

PB is the distance of fire station P from the building

QB is the distance of fire station Q from the building

Distance between P and Q is 20 m

So, Let PB = x

So, QB = 20-x

In ΔAPB

$Tan\tehta = \frac{Perpendicular}{Base}$

$Tan 60^{\circ} = \frac{AB}{PB}$

$\sqrt{3} = \frac{AB}{x}$  --1

In ΔABQ

$Tan\tehta = \frac{Perpendicular}{Base}$

$Tan 45^{\circ} = \frac{AB}{QB}$

$20-x = AB$  --2

So, Comparing 1 and 2

$20-x = \sqrt{3}x$

$20 =( \sqrt{3}+1)x$

$\frac{20}{\sqrt{3}+1}=x$

$7.320=x$

So, PB = 7.320 km

QB = 20-7.320 =12.68 km

So. it should send team to Station P since the distance between building and P station is less than the distance between Q station and building

So, team has to travel 7.320 km