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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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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