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.
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∘=ABAP⇒√3=hAP⇒AP=h√3 In ΔQAB, we have tan45∘=ABAQ⇒1=hAQ⇒AQ=h Now, PQ=20 km ⇒AP+AQ=20⇒h√3+H=20⇒h+√3h√3=20⇒h(1+√3)=20√3⇒h=20√31+√3⇒h=20√31+√3×1−√31−√3⇒h=20√3−601−3⇒h=30−10√3⇒h=10(3−√3)⇒h=12.68km Now, in triangle APB, sin60∘=AB/BP √32=hBP This gives h= 14.64 km