The horizontal distance between A\ B and C\ ...

ICSE Class X Math 2013 Paper

In the figure given, from the top of a building $A B = 60\,\mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $C D$ are observed to be $30^{\circ}$ and $60^{\circ}$ respectively. Find :

Question : 30 of 46

Marks: +1, -0

The horizontal distance between

A\ B

and

C\ D

Solution:

Given :

AB=60\,\text{m}

\; \because\;\; \angle P PAC = 60^{\circ}

\; \therefore\;\; \angle PAC = \angle BCA

Now in

\triangle ABC

\tan 60^{\circ}\;=\;\frac{AB}{BC}

\sqrt{3}\;=\;\frac{60}{BC}

\Rightarrow\; BC = \frac{60}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}

BC = \frac{60\sqrt{3}}{3}=20\sqrt{3}\,\text{m}

Hence, the horizontal distance between

AB

and

CD=20\sqrt{3}\,\text{m}

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