Question

A man finds the angle of elevation of the top of the tower to be 30 degrees. It walks 85 meter nearer the tower and find its angle of elevation to be 60 degrees. What is the height of tower?

Answer 1

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

$\green{\therefore{\text{Height\:of\:tower=42.5}\sqrt{3}\:m}}$

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

• In the given question information given about a man finds the angle of elevation of the top of the tower to be 30 degrees. It walks 85 meter nearer the tower and find its angle of elevation to be 60 degrees.

• We have to Find the height of tower.

$\green{\underline \bold{Given :}} \\ : \implies \text{Angle \: of\:elevation=} 30^{\circ} \\ \\ : \implies \text{Angle\:of\:elevation\:of\:tower\:after\:walking\:85\:m\:towards\:tower= }60^{\circ}\\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Height\:of\:tower= ?}$

• According to given question :

$\text{Let\:Height\:of\:tower\:be\:x}\\\\ \bold{In \: \triangle \: ABC} \\ : \implies tan\:\theta=\frac{\text{perpendicular}}{\text{base}}\\ \\ : \implies tan\:30^{\circ} = \frac{AB}{BC} \\ \\ : \implies \frac{1}{\sqrt{3}}=\frac{x}{BD+85}\\ \\ : \implies BD+85=\sqrt{3} x\\ \\ : \implies BD = \sqrt{3}x-85-----(1)\\\\\bold{In\:\triangle\:ABD}\\ :\implies tan\:\theta=\frac{p}{b} \\\\ :\implies tan\:60^{\circ}=\frac{AB}{BD}\\\\ :\implies \sqrt{3}=\frac{x}{BD}\\\\ :\implies BD=\frac{x}{\sqrt{3}}-----(2)\\\\ \bold{from\:(1)\:and\:(2)}$

$: \implies \sqrt{3} x - 85 = \frac{x}{ \sqrt{3} } \\ \\ : \implies ( \sqrt{3}x - 85) \sqrt{3} = x \\ \\ : \implies 3x - 85 \sqrt{3} = x \\ \\ : \implies 2x = 85 \sqrt{3} \\ \\ : \implies x = \frac{85 \sqrt{3} }{2} \\ \\ \green{: \implies x = 42.5 \sqrt{3} \: m} \\ \\ \green{\therefore \text{height \: of \: tower = 42.5} \sqrt{3} \: m}$