Question

A kite is flying, attached to a thread which is 165m long. The thread makes an angle of `30^(@)` with the ground. Find the height of the kite from the ground , assuming that there is no slack in the thread.

Answer 1

Let OX be the horizontal ground and let A be the position of the kite. Let O be the position of the observer and OA be the thread. Draw `AB_|_OX`.
Then, `angleBOA = 30^(@), OA = 165 m` and `angleOBA = 90^(@)`
Height of the kite from the ground `= AB`.
Let `AB = h` metres.
From right `DeltaOBA`, we have
`(AB)/(OA) = sin 30^(@) = 1/2`
`rArr h/165 = 1/2 rArr h = 165/2 = 82.5`.
Hence, the height of the kite from the ground `= 82.5 m`.