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प्रश्न
Two persons standing on opposite sides of a tower observe the angles of elevation of the top of the tower to be 60° and 50° respectively. Find the distance between them, if the height of the tower is 80m.
उत्तर
Let the position of the two persons be A and C. Let BD be the tower of height 80 m.
In ΔBAD,
`tan60^circ = "BD"/"AD"`
⇒ `sqrt(3) = 80/"AD"`
⇒ `"AD" = 80/sqrt(3)`
⇒ AD = `(80sqrt(3))/3 = (80 xx 1.732)/3` = 46.19 ...(1)
In ΔBDC,
`tan50^circ = "BD"/"DC"`
⇒ `1.1918 = 80/"DC"`
⇒ `"DC" = 80/1.1918 = 67.13` ....(2)
:. AC = AD + DC = 46.19 m + 67 .13 m = 113.32 m
Thus, the horizontal distance between the two persons is 113. 32 m.
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