Question

An aeroplane flies from the ground making an angle of 30° with the ground and covers a distance of 184 m. What will be the height of the aeroplane above the ground?

Answer 1

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

$\green{\tt{\therefore{Height\:of\:aeroplane\:above\:the\:ground=92\:m}}}$

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

$\green{\underline \bold{Given:}} \\ \tt: { \implies Distance\:travelled\:by\:aeroplane=184\:m}\\\\ \tt:\implies Angle\:of\:elevation=30\degree\\\\ \red{\underline \bold{To \: Find:}} \\ \tt: {\implies Height\: of \:aeroplane\:above\:the\:ground= ?}$

• According to given question :

$\circ \: \tt{Let \: Height\: of\:aeroplane\:from\:the\:ground \: be\: h } \\ \\ \bold{As \: we \: know \: that} \\ \tt: {\implies sin \: \theta= \frac{Perpendicular}{Hypotenuse} }\\ \\ \tt:{ \implies sin\:30\degree = \frac{h}{184}}\\\\ \tt:{\implies \frac{1}{2}=\frac{h}{184} }$

$\tt: \implies \frac{1}{ 2 } \times 184 = h \\ \\ \tt: \implies \frac{184}{2} = h$

$\tt: { \implies 92 = h }\\ \\ \green{\tt: \implies h = 92\:m} \\ \\ \green{\tt {\therefore Height \: of\: aeroplane \: above \: the\:ground\:is 92 \:m}}$

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

Answer 2

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