Question

from a window 9m above the ground of a house in a street the angles of elevation and depression of the foot of another house on the opposite side of the street are 30 degree's and 60 degree's respectively find the height of the opposite house and width of the street​

Answer 1

height of building is 12m

Answer 2

The total height of the opposite house is 12 m and  width of the street is  $3{\sqrt{3}$.

Step-by-step explanation:

Given:

We assume that P be the window and PE be the width of the street.

Also height of the house = (h + 9) m.

As shown in the figure below, PE = BC = d.

PE= DC = 9 m and ∠APE = 30° and ∠BPE = 60°.

So, AB = (h + 9) m. and AE = h m.

Now, in ΔAPE

$tan 30 =\frac{h}{d}$

$\frac{1}{\sqrt{3} }=\frac{h}{d}$

∴  $h=\frac{d}{\sqrt{3}}$

Also, in ΔBPE

$tan 60 =\frac{9}{d}$

 $\sqrt{3}=\frac{9}{d}$

∴  $d=\frac{9}{\sqrt{3}}$

∴  $d=3{\sqrt{3}$

Therefore, width of the street = $d=3{\sqrt{3}$.

$h=\frac{d}{\sqrt{3}}=\frac{3\sqrt{3}}{\sqrt{3}}=3$

h = 3 m.

Hence the total height of the opposite house = h + 9 = 3 + 9 = 12 m.