Question

A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30°. From the bottom of the same building, the angle of elevation of kite is 45°. Find the length of the string and height of roof from the ground. (Use `sqrt(3) = 1.73`)

Answer 1

Let the building be AB with height h.

Let the kite be at point K at height 60 m.

From the bottom of the building (point A):

In △KAC (where C is on the ground below kite):

`tan 45^circ = 60/x`

⇒ `1 = 60/x`

⇒ x = 60 m

From the roof (point B):

The height of the kite above the roof is (60 – h).

In the right triangle formed with the roof level:

`tan 30^circ = (60 - h)/x`

`1/sqrt(3) = (60 - h)/60`

`60 - h = 60/sqrt(3)`

`60 - h = 20sqrt(3)`

h = 60 – 20(1.73)

= 60 – 34.6 

= 25.4 m

Now, to find the length of the string (s) from Ravi:

`sin 30^circ = (60 - h)/s`

`1/2 = (20sqrt(3))/s`

`s = 40sqrt(3)`

= 40 × 1.73

= 69.2 m

The height of the roof is 25.4 m and the length of the string is 69.2 m.