Question

the angle of elevation of the top of a pillar point c on the ground is 30⁰and on walking 100m towards the pillar the angle becomes 60⁰. find the height of the pillar and its distance from point c

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Height\:of\:pillar=50\sqrt{3}\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt:\implies Angle \: of \: elevation( \theta) = 30 \degree \\ \\ \tt:\implies Angle \: of \: elevation( \theta_{o} ) = 60 \degree \\ \\ \tt: \implies Distance \: DC = 100 \: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Height \: of \: pillar =?$

• According to given question :

$\tt \circ \: Let \: height \: of \: pillar \:be \: x \\ \\ \bold{In \: \triangle \: ABC : } \\ \tt: \implies tan \: \theta = \frac{p}{b} \\ \\ \tt: \implies tan \:30 \degree = \frac{AB}{BC} \\ \\ \tt: \implies \frac{1}{ \sqrt{3} } = \frac{x}{BD + DC} \\ \\ \tt: \implies \frac{1}{ \sqrt{3} } = \frac{x}{BD+ 100} \\ \\ \tt: \implies BD+ 100 = \sqrt{3} x \\ \\ \tt: \implies BD = \sqrt{3} x - 100 - - - - - (1) \\ \\ \bold{In \: \triangle \: ABD: } \\ \tt: \implies tan \: \theta_{o} = \frac{p}{b} \\ \\ \tt: \implies tan \: 60 \degree = \frac{AB}{BD} \\ \\ \tt: \implies \sqrt{3} = \frac{x}{ \sqrt{3} x - 100} \\ \\ \tt: \implies 3x - 100 \sqrt{3} = x \\ \\ \tt: \implies 3x - x = 100 \sqrt{3} \\ \\ \tt: \implies 2x = 100 \sqrt{3} \\ \\ \tt: \implies x = \frac{100 \sqrt{3} }{2} \\ \\ \green{\tt: \implies x = 50 \sqrt{3} \: m} \\ \\ \green{\tt \therefore Height \: of \: pillar \: is \: 50 \sqrt{3} \: m}$