If the angle of elevation of a kite is `60^(@)` and the length of thread is `20sqrt(3)` meters, calculate the height of kite above the ground.

Explanation

Let the height of the kite be AB = h metre anove the ground and let AC be the thread.
As per question, AC `= 20sqrt(3)` metres and `angleACB` = angle of elevation of the kite at `A = 60^(@)`.
Now, from right-angled triangle ABC,
`sin angleACB = sin 60^(@) = (AB)/(AC) ` [ by definition of `sintheta`]
or, `(sqrt(3))/(2) =(h)/(20sqrt(3)) " " or, 2h = 20xx3 " " or, h = (20xx3)/(2) = 30`
Hence the required height of the kite above the ground = 30 metres.