Question

A kite is flying at a height of 60 m above the ground. the string attached to the kite is temporarily tied to a point on the ground. the inclination of the string with the ground is 60°. find the length of the string, assuming that there is no slack in the string.

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Q - Position of kite at height 60m above the ground

RQ = 60 m

Assume O be the point on ground in which string is tied

Therefore

Length = OQ

∠ROQ = 60

Now,

In right angle triangle ORQ :-

$\tt{\rightarrow\dfrac{RQ}{OQ}=sin60}$

Or,

$\tt{\rightarrow OQ=\dfrac{RQ}{sin30}}$

OQ = RQ cosec60

l = OQ

$\tt{\rightarrow 60\times\dfrac{2}{\sqrt{3}}}$

$\tt{\rightarrow\dfrac{120}{\sqrt{3}}}$

= 40√3 m

Therefore we get :-

Length of string is 40√3

Answer 2

$\huge \sf \green{ \bigstar \: Hello \: Mate \bigstar}$

AB represents the distance of a kite from ground.

∴ AB = 60 m

seg AC represents the length of the string

m ∠ ACB = 60º

In right angled ∆ ABC,

sin 600 = side opposite to 600/Hypotenuse

∴ sin 600 = AB/AC

∴ √3/2 = 60/AC

∴ AC = 120/√3

∴ AC = (120/√3)× (√3/√3)

∴ AC = 40√3 m

∴ AC = 40 × 1.73

∴ AC = 69.2 m