Question

a man observes the angle of elevation of tower is 30° after advancing 11 m towards it he observes that the angle of elevation is 45° find height of the tower​

Answer 1

Answer:

15 m is the answer of your questions

Answer 2

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

$\green{\therefore{\text{Height\:of\:tower=5.5}(\sqrt{3}+1)\:m}}$

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

• In the given question information given about a man observes the angle of elevation of tower is 30° after advancing 11 m towards it he observes that the angle of elevation is 45°.

• We have to Find the height of tower.

$\green{\underline \bold{Given :}} \\ : \implies \text{Angle \: of\:elevation= }30^{\circ} \\ \\ : \implies \text{Angle\:of\:elevation\:of\:tower\:after\:walking\:11\:m\:towards\:tower=} 45^{\circ} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Height\:of\:tower= ?}$

• According to given question :

$\text{Let\:Height\:of\:tower\:be\:x}\\\\ \bold{In \: \triangle \: ABC} \\ : \implies tan\:\theta=\frac{\text{perpendicular}}{\text{base}}\\ \\ : \implies tan\:30^{\circ} = \frac{AB}{BC} \\ \\ : \implies \frac{1}{\sqrt{3}}=\frac{x}{BD+11}\\ \\ : \implies BD+11=\sqrt{3} x\\ \\ : \implies BD = \sqrt{3}x-85-----(1)\\\\\bold{In\:\triangle\:ABD}\\ :\implies tan\:\theta=\frac{p}{b} \\\\ :\implies tan\:45^{\circ}=\frac{AB}{BD}\\\\ :\implies 1=\frac{x}{BD}\\\\ :\implies BD={x}-----(2)\\\\ \bold{from\:(1)\:and\:(2)}$

$: \implies \sqrt{3} x - 11 = {x} \\ \\ : \implies \sqrt{3}x -x =11 \\ \\ : \implies x(\sqrt{3}-1)=11\\ \\ : \implies x = \frac{11 }{(\sqrt{3}-1)} \\ \\ \green{: \implies x = 5.5 (\sqrt{3} +1)\: m} \\ \\ \green{\therefore \text{height \: of \: tower = 5.5}(\sqrt{3}+1)\:m}$