Question

When the ratio of the height of a telephone pole and the length of its shadow is root 3:1, find the angle of elevation of the sun.

Answer 1

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

$\green{\tt{\therefore{Angle\:of\:elevation\approx71.6\degree}}}$

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

$\green{\underline \bold{Given:}} \\ \tt: { \implies Height:Shadow\:of\:pole=3:1} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: {\implies Angle \: of \: elevation = ?}$

• According to given question :

$\circ \: \tt{Let \: angle \: of \: elevation \: of \: \: pole \: be\: \alpha } \\ \\ \bold{As \: we \: know \: that} \\ \tt: {\implies tan \: \alpha = \frac{Perpendicular}{Base} }\\ \\ \tt:{ \implies tan \: \alpha = \frac{3x}{x}}\\\\ \tt:{\implies tan\:\alpha=\frac{3}{1} }$

$\tt: { \implies \alpha = {tan}^{ - 1} ( 3) }\\ \\ \tt \circ \: tan \: 71.6 \degree \approx 3\\ \\ \green{\tt: \implies \alpha \approx 71.6\degree} \\ \\ \green{\tt {\therefore Angle \: of \: elevation \: of \: pole \: to \: ground \: is \:\approx71.6 \degree}}$

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

Answer 2

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