From a window 'h' m high above the ground of a house on a street, the angle of elevation and depression of the top and foot of another house on the opposite side of the street are $α$ and $β$ respectively.
The height of the opposite house is ___

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Solution

The correct option is A
3

Let the height of the other house be DC
DC=(h+y)m

Let the distance between the two houses = x

In $Δ B F C$

$t a n β = \frac{h}{x}$

$x = \frac{h}{t a n β} \dots (i)$

In $Δ B F D$

$t a n α = \frac{y}{x}$

$t a n α = \frac{y}{\frac{h}{t a n β}}$ ......from (i)

$t a n α = \frac{y t a n β}{h}$

$∴ y = \frac{h t a n α}{t a n β}$

Height of the other house = h+y

$= h + h \frac{t a n α}{t a n β}$

$= h (1 + \frac{t a n α}{t a n β})$

$= h (1 + t a n α c o t β)$

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From a window 'h' m high above the ground of a house on a street, the angle of elevation and depression of the top and foot of another house on the opposite side of the street are α and β respectively. The height of the opposite house is ___

From a window 'h' m high above the ground of a house on a street, the angle of elevation and depression of the top and foot of another house on the opposite side of the street are $α$ and $β$ respectively.
The height of the opposite house is ___