A kite is flying at a height of 60 m above the ground. The string arrached 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.

Explanation

Let A represent the position of kite.
seg BD represent the surface of the ground.
seg AB is the height of the kite above the ground.
AB = 60
`angleADB` is the angle made by the string with the ground.
`angleADB = 60^@`
In right angled `triangle`ABD,
`sin 60^@ = (AB)/(AD) ` .... (By definition )
`therefore sqrt(3)/2 = 60/(AD)` ....`(therefore sin 60^@ = sqrt(3)/2 )`
`therefore AD xx sqrt(3) = 60 xx 2`
` therefore AD = (60 xx 2)/(sqrt(3))`
`therefore AD = (120)/(sqrt(3) xx sqrt(3)/(sqrt(3)`
`therefore AD = (120sqrt(3))/(3) `
`therefore AD = 40sqrt(3)`
`therefore AD = 40 xx 1.73` ....(`because sqrt(3) = 1.732)`
`therefore` AD = 69.2 m
The length of the string is 69.2 m.