Aspire Faculty ID #11968 · Topic: NIMCET 2025 · Just now
NIMCET 2025

The angles of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30° and 45°, respectively. What is the height of the multistoried building and the distance between the two buildings?

Solution

The height of the multistoried building is $H$ and the horizontal distance between the buildings is $D$. 
The angles of depression to the top and bottom of the $8\text{ m}$ building are $30^\circ$ and $45^\circ$ respectively. 
From the $45^\circ$ angle: 
$\tan 45^\circ = \dfrac{H}{D}$ 
$1 = \dfrac{H}{D}$ 
$H = D$ 

From the $30^\circ$ angle: 
$\tan 30^\circ = \dfrac{H - 8}{D}$ 
$\dfrac{1}{\sqrt{3}} = \dfrac{H - 8}{H}$ 
$H - 8 = \dfrac{H}{\sqrt{3}}$
$H\left(1 - \dfrac{1}{\sqrt{3}}\right) = 8$ 
Solve for $H$: 
$H = \dfrac{8}{1 - \dfrac{1}{\sqrt{3}}}$ 
$H = 4(3 + \sqrt{3})$ 
Since $H = D$: 
$D = 4(3 + \sqrt{3})$ 
Final answers: 
$\boxed{H = 4(3 + \sqrt{3})\ \text{m}}$ 
$\boxed{D = 4(3 + \sqrt{3})\ \text{m}}$
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