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Home » 1. The distance of the gate of a temple from its base is     times it height. Find the angle of elevation of the top of the temple.
1. The distance of the gate of a temple from its base is

    \[\sqrt{3}\]

times it height. Find the angle of elevation of the top of the temple.
Class 10 | Frank | Guides | Heights and Distances | ICSE | Maths
1. The distance of the gate of a temple from its base is

    \[\sqrt{3}\]

times it height. Find the angle of elevation of the top of the temple.

Let us assume that PQ be the temple and R be the position of gate of the temple.

Let us assume “h” be the height of the temple,

Then, PQ = h

QR = Distance of the gate of temple from its base =

    \[\sqrt{3}h\]

In ΔPQR,

\tan \theta = \frac{PQ}{QR}

\tan \theta = \frac{h}{\sqrt{3}h}

\tan \theta = \frac{1}{\sqrt{3}}

So as we known,

\tan {{30}^{\circ }}

    \[=\frac{1}{\sqrt{3}}\]

  

Therefore on comparing, \theta ={{30}^{\circ }}

Hence, the angle of elevation from the top of the temple is

    \[{{30}^{\circ }}\]

.

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