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Question
From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take `sqrt3` = 1.732)
Solution
Let AB be the flag of length hm on the building BC.
We assume that BC = 10, ∠APC = 45°, ∠BPC = 30°
Now we have to find height of flag-staff and distance of the point P from the building
The corresponding figure is as follows
In a triangle BPC,
`=> tan "P" = ("BC")/("CP")`
`=> tan 30^@ = ("BC")/("CP")`
`=> "CP"="BC"/tan30^@`
`=> 10/(1/sqrt3)`
`= 10sqrt3` m
Again in a triangle ACP
`=> tan "P" = ("AC")/"CP"`
`=> 1 = ("AC")/"CP"`
`=>` AC = CP = 10`sqrt3` m
`=>` AB + BC = CP
`=>` x = 10 = 10`sqrt3`
`=> x = 10sqrt3-10`
`=>10(sqrt3-1)`
= 10 × 0.73
h = 7.32
Hence the length is 17.32 m and distance is 7.32 m
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