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प्रश्न
The angles of depression of two cars on a straight road as observed from the top of a 42m high building are 60° and 75° respectively. Find the distance between the cars if they are on opposite sides of the building.
उत्तर
Let the position of the two cars be A and C. Let BO be the building of height 42 m.
In ΔBAD,
`tan75^circ = "BD"/"AD"`
⇒ `3.7321 = 42/"AD"`
⇒ `"AD" = 42/3.7321`
⇒ AD = 11.25 ....(1)
In ΔBDC,
`tan60^circ = "BD"/"DC"`
⇒ `sqrt(3) = 42/"DC"`
⇒ `"DC" = 42/1.732 = 24.25` ....(2)
∴ AC = AD+ DC = 11.25 m + 24.25 m = 35.5 m
Thus, the distance between the cars is 67.63 m.
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