Question

from the top of a hill 200 metre height the angle of dispression of the top & the bottom of pillar are 30° and 60° respectively. Find the pillar's height and its distance from the hill

Answer 1

Description for Correct answer:


AB = hill = 200 metre

CD = tower

\( \Large In\triangle APC \)

\( \Large tan30 ^{\circ}=\frac{AP}{PC} \)

\( \Large \frac{1}{\sqrt{3}}=\frac{AP}{PC}\Rightarrow AP:PC=1:\sqrt{3}......(i) \)

\( \Large In\triangle ABD \)

\( \Large tan60 ^{\circ} =\frac{AB}{BD} \)

\( \Large \sqrt{3}=\frac{AB}{BD}=AB:BD=\sqrt{3}:1......(ii) \)

PB = CD and PC = BD

Now



\( \Large CD=PB\Rightarrow AB-AP \)

\( \Large CD=3-1=2\ units \)

\( \Large AB=3\ units=200\ metre \)

\( \Large CD=2\ units=\frac{200}{3} \times 2 \)

\( \Large =133\frac{1}{3}\ metre\)