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Question

A fire in the building is reported to 2 diff fire stations p and q.pobserves the fire is on an angle of 60 deg.and q observes it on 45°.if both stations are 20 km apart then find the dist. Which team p will have to cover to reach the tower.


Solution



Let AB be the building of height h, Clearly APB>AQB.
APB>ABQ
AP<AQ
Station P is nearer to the building
So, station P must send its team.
In ΔAPB, we have
tan60=ABAP3=hAPAP=h3
In ΔQAB, we have
tan45=ABAQ1=hAQAQ=h
Now, PQ=20 km
AP+AQ=20h3+H=20h+3h3=20h(1+3)=203h=2031+3h=2031+3×1313h=2036013h=30103h=10(33)h=12.68km
Now, in triangle APB,
sin60=AB/BP
32=hBP
This gives h= 14.64 km

All India Test Series

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