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Dr. Bansal needs to determine the distan...

Dr. Bansal needs to determine the distance PQ across a river in and east-west direction as shown in the adjoining figure. He can't measure this distance directly over the water. So, he selects the point S from where a straight line to point Q stays on land so he can mesure distance. he then moves eastward a distance of 400 m from point S to T , so that the line of sight from point T to P cuts the previous line SQ at R. finally with a long measuring tape. he determines that.
SR = 250 m, QR= 1250 m
Determine if this is enough information to calculate the distance PQ and if so, find PQ and hence find the time taken by a swimmer to cross the river PQ with a uniform speed of 800 m/hr.

Text Solution

Verified by Experts

In `triangleSRT and trianglePQR`
` angle3=angle4` ( vertically oppostie angles)
`angle1=angle2` ( alternate angles)
` triangleSRT~triangleQRP` ( AA corollary)
`(SR)/(QR)= (RT)/(RP)=(ST)/(QP)` (corresponding sides of similar triangles are proportional)
( since he moves eastward, a distance of 400 m from point S )
`Rightarrow PQ= (400xx1250)/250=2000 m `
Hence, width of the river= 2000 m
A swimmer swims 800 m in 60min.
A swimmer swims 1 m in `60/800` min
A swimmer swims 2000 m in `60/800 xx 2000 min`
150 min = 2 hr and 30 minutes.
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