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प्रश्न
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
उत्तर
Consider RZ as the building, XR as the flag, and Y as the ground point from which the elevation angles are to be measured.
So, RZ = 25 m, ∠XYZ = 60°, ∠RYZ = 30°.
Now, in ΔRYZ,
`(RZ)/(YZ)` = tan 30°
⇒ `25/(YZ) = 1/sqrt(3)`
⇒ YZ = `25sqrt(3)` m
Also, in ΔXYZ,
`(XZ)/(YZ)` = tan 60°
`(XR + RZ)/(YZ) = sqrt(3)`
`(XR + 25)/(25sqrt(3)) = sqrt(3)`
XR + 25 = `25sqrt(3) xx sqrt(3)`
XR + 25 = 75
XR = 75 – 25 = 50
As a result, the flag's height is 50 metres.
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