A fire in a building B...

 A fire in a building B is reported 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?



Comments

  1. UnknownNovember 30, 2020 at 1:52 PM

    Station P should send it's team because it will have to travel a distance of 7.3 km which is less than 12.7 km which the team of station Q would have to travel.

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  2. AnonymousDecember 1, 2020 at 2:12 PM

    So two right triangles are formed on both sides , P team having theta as 60 degrees while Q having theta as 45 degrees.Let the distance from P be x , so the distance from Q becomes 20-x as P and Q are 20 km apart as given in the question.Both triangles have common perpendicular .
    From Team P perspective the perpendicular can be found by tan 60 = p/x == root 3* x=p
    and from Team Q perspective the perpendicular tan 45= p/20-x == 20-x=p

    So on equating for p, x= 20/root 3+1 == x=20/1.73+1== x=20/2.73== x=7.32 km

    From P it is 7.32 km
    While from Q =20-x ==20-7.32 = 12.68 km

    Hence it is clear that Team P must be sent as it needs to cover a shorter distance that is 7.32 km instead of Team Q which has to travel a distance of 12.68 km .
    Hence Team P will take lesser time.

    ReplyDelete
  3. AnonymousDecember 1, 2020 at 2:13 PM

    (So two right triangles ....)

    ~By Kriishh Gada

    ReplyDelete
  4. UnknownDecember 1, 2020 at 3:23 PM

    Two right triangles are formed where the angle from the Station P is 60 degrees and that from Station Q is 45 degrees.
    Let the distance from station P be x km and that from station Q be (20-x) km since the distance between station Q and Station P is 20 km.

    tan 60 = height of building/x km , therefore x root 3 =height of building _(1)

    tan 45 = height of building/(20-x) km , therefore 20-x = height of building _(2)

    From (1) and (2) ,
    20-x = x root 3, therefore x=7.32 km and 20-x=12.68 km .

    Therefore station P must send its team as it will take less time to reach the destination.

    -By Somil Kashyap

    ReplyDelete
  5. UnknownDecember 1, 2020 at 7:18 PM

    Two right triangles are formed where the angle from the Station P is 60 degree and that from Station Q is 45 degree.
    Let the distance from station P be x km
    Let distance from station Q be (20-x) km since the distance between station Q and Station P is 20 km.(given)

    tan 60 = height of building/x km
    x root 3 =height of building ---------(1)

    tan 45 = height of building/(20-x) km
    therefore 20-x = height of building ------ (2)

    From (1) and (2) ,
    20-x = x root 3
    thus x=7.32 km
    20-x=12.68 km .

    Therefore station P must send its team as it will take less time to reach the destination by 5.36 km

    ReplyDelete
  6. UnknownDecember 1, 2020 at 7:19 PM

    yuvika mahajan class 10 -g

    ReplyDelete
  7. AnonymousDecember 1, 2020 at 9:15 PM

    Bravo kids.

    ReplyDelete
  8. Sanjam BediDecember 2, 2020 at 9:17 AM

    We get two right angled triangles on a straight road which are 20km apart from each other.
    Let the distance of station P =x km
    Therefore the distance of station Q becomes (20-x) km.

    tan 60 = height of building/x km
    x root 3 =height of building →(1)

    tan 45 = height of building/(20-x) km
    therefore 20-x = height of building→(2)

    Equating (1) and (2), we get:
    20-x = x root 3

    thus x=7.32 km
    20-x=12.68 km .

    Therefore station P must send its team as it will take less time to reach the destination by 5.36km

    Sanjam Bedi
    10-B

    ReplyDelete

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