Question

The length of a string between a kite and a point on the ground is 90 m. If the string makes an angle θ with the level ground such that tanθ= 15/8 . Find the height of the kite.

Answer 1

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

$\green{\tt{\therefore{Height\:of\:kite=78.3\:m}}}$

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

$\green{\underline \bold{Given:}} \\ \tt: { \implies Length\:of\:string=90\:m}\\\\ \tt:\implies Angle\:of\:elevation=\theta\\\\ \tt:\implies tan\:\theta=\frac{15}{8} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: {\implies Height \: of \:kite= ?}$

• According to given question :

$\tt\circ\:\theta=tan^{-1}(\frac{15}{8})\approx 61.2\degree \\\\ \circ \: \tt{Let \: Height\: of \: kite \: be\: h } \\ \\ \bold{As \: we \: know \: that} \\ \tt: {\implies sin \: \theta= \frac{Perpendicular}{Hypotenuse} }\\ \\ \tt:{ \implies 0.87 = \frac{h}{90}}\\\\ \tt:{\implies 0.87\times 90=h }$

$\tt: { \implies 78.3 = h }\\ \\ \green{\tt: \implies h = 78.3\:m} \\ \\ \green{\tt {\therefore Height \: of \:kite \: is \:78.3 \:m}}$

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

Answer 2

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