A vertical pole is divided by any point in the ratio 9:1. If both the segments subtend equal angles to each other at a point 20m away from the foot of the pole , find the height of the pole?

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Answer 1 · 2018-08-05T16:04:28

Let the lengths of two parts be $9 x and x$ $9xand x$ m.

So total length will be $10 x$ $10x$ m

So length of hypotenuse $= \sqrt{20^{2} + 100 x^{2}}$ $=sqrt(20^2+100x^2)$ m

As the angles subtended by two parts at 20 m distance from the foot are same, we can write

$\frac{\sqrt{20^{2} + 100 x^{2}}}{20} = \frac{9}{1}$ $sqrt(20^2+100x^2)/20=9/1$

$\Rightarrow \frac{20^{2} + 100 x^{2}}{400} = 81$ $=>(20^2+100x^2)/400=81$

$\Rightarrow 100 x^{2} = 81 \times 400 - 400 = 80 \times 400$ $=>100x^2=81xx400-400=80xx400$

$\Rightarrow x = \sqrt{320} = 8 \sqrt{5}$ $=>x=sqrt320=8sqrt5$

So length of the pole $= 80 \sqrt{5}$ $=80sqrt5$ m