Question

The shadow of Qutab Minar is 81 m long when the angle of elevation of the Sun is θ. Find the height of the Qutab Minar if tanθ= 0.89.

Answer 1

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

$\green{\tt{\therefore{Height\:of\:Qutab\:minar=72.09\:m}}}$

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

$\green{\underline \bold{Given:}} \\ \tt: { \implies Shadow\:of\:Qutab\:minar=81\:m}\\\\ \tt:\implies Angle\:of\:elevation=\theta\\\\ \tt:\implies tan\:\theta=0.89 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: {\implies Height \: of \: Qutab\:minar= ?}$

• According to given question :

$\circ \: \tt{Let \: Height\: of \: Qutab \:minar \: be\: h } \\ \\ \bold{As \: we \: know \: that} \\ \tt: {\implies tan \: \theta= \frac{Perpendicular}{Base} }\\ \\ \tt:{ \implies 0.89 = \frac{h}{81}}\\\\ \tt:{\implies 0.89\times 81=h }$

$\tt: { \implies 72.09 = h }\\ \\ \green{\tt: \implies h = 72.09\:m} \\ \\ \green{\tt {\therefore Height \: of \: Qutab \: minar \: is \:72.09 \:m}}$

$\blue{ \bold{Some \: property \: of \: trigonometery}} \\ \orange{\tt {\circ \: sin \: \alpha = \frac{Perpendicular}{Hypotenuse}} } \\ \\ \orange{\tt{ \circ \: cos \: \alpha = \frac{Base}{Hypotenuse}} } \\ \\ \orange{\tt{ \circ \: cot \: \alpha = \frac{Base}{Hypotenuse}} } \\ \\ \orange{\tt {\circ \: cosec \: \alpha = \frac{Hypotenuse}{Perpendicular} }} \\ \\ \orange{\tt {\circ \: sec \: \alpha = \frac{Hypotenuse}{Base} }}$

Answer 2

$\large \underline{ \blue{ \boxed{ \bf \green{Required \: Answer}}}}$