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An aeroplane id flying at a height of 3...

An aeroplane id flying at a height of 300 m above the ground. Fying at this height , theangles of depression from the aeroplane of two points on both banks of a river in opposite directions are `45^(@)" and "60^(@)` respectively. Find the width of the river.[use `sqrt3=1.732`]

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let an aeroplane P is flying at a height of 300 m above the ground
`:. PM=300 m`
Depression angles are `angleXPA=45^(@)" and "angle YPB=60^(@)`. ,brgt `:. anglePAM=45^(@)" and " angle PBM=60^(@)" (alternate angles)"`
Now, in right `DeltaPMA`,
`tan45^(@)=(PM)/(AM)rArr1=300/(AM)rArrAM=300 m ...(1)`
In right `DeltaPMB`,
`tan60^(@)=(PM)/(MB)rArrsqrt3=300/(MB)rArrMB=300/sqrt3=100sqrt3 ...(2)`
`:. " WIdth of river "=AM+MB`
`=(300+100sqrt3)m=(300+100xx1.732)m`
`=(300+173.2)m=473.20m`
Hence, the width of the river -473.20 m
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