A fire is reported in a building. There are two fire stations on either side of the building and in the same straight line with it. The elevation of the building from the stations A and B are 30o and 60o respectively. Which fire station is closer to the building?
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30° is closer and 60° is further
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Answer :
We form our diagram , As :
Here CD is height of building
And
Let AC is distance from stations A ,and BC is distance from station B of building CD.
In ∆ACD,tan 30° = DCAC⇒13√ = DCAC⇒AC = 3‾√DC = 1.732DC .....(1)In ∆BCD,tan 60° = DCBC⇒3‾√ = DCBC⇒BC = DC3√ = 3√DC3 =1.732DC3 = 0.577DC .....(2)From (1) and (2), we getBC <AC.Hence station B is more closer to the building than station A.
We form our diagram , As :
Here CD is height of building
And
Let AC is distance from stations A ,and BC is distance from station B of building CD.
In ∆ACD,tan 30° = DCAC⇒13√ = DCAC⇒AC = 3‾√DC = 1.732DC .....(1)In ∆BCD,tan 60° = DCBC⇒3‾√ = DCBC⇒BC = DC3√ = 3√DC3 =1.732DC3 = 0.577DC .....(2)From (1) and (2), we getBC <AC.Hence station B is more closer to the building than station A.
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