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✔from a window 9 m above the ground of a house in a street the angle of elevation and depression of the top and foot of another house on the opposite side of the street are 30° and 60° respectively find the height of the opposite house and the width of the street .
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Step-by-step explanation:
let D be the window and DE be the width of the street.
And height of the house = (h + 9) m.
In the above figure DE = CB = d. BE= DC = 9 m and ∠ADE = 30°
and ∠BDE = 60°.
AB = (h + 9) m.
and AE = h m.
In a ΔADE Tan 30° = h / d 1 / √3 = h / d ∴ h = d / √3.
In a ΔBDE Tan 60° = 9 / d √3 = 9 / d ∴ d = 9 / √3 = 3√3.
∴ Width of the street = 3√3. h = d / √3 = 3√3 / √3 = 3 h = 3 m.
∴ total height of the house = h + 9 = 3 + 9 = 12 m.
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