Shib is flying kite having the length of thread 250 metres, when the thread makes an angle `60^(@)` with the horizontal line and when the thread makes an angle of `45^(@)` with the horizontal line. Calculate in each case what is the height of kite from the ground. Also find in which of the two cases will the kite be at a greater height from the other.

Explanation

Let the height of the kite when the thread of length 250 metres makes an angle `60^(@)` with the horizontal line is AB and when `45^(@)` is CD.
As per question, OA = OC = 250 m.
Now, from the right-angled triangle OAB we get,
`sin 60^(@) = (AB)/(OA)` [ by definition ]
or, `(sqrt(3))/(2)=(AB)/(250)" " or, " " 2AB = 250sqrt(3)`
or, `AB = (250sqrt(3))/(2) = 125sqrt(3)`
Again, from the triangle OCD(right-angled) we get,
`sin 45^(@) = (CD)/(OC)`
or, `(1)/(sqrt(2))=(CD)/(OC) " "or, " " OC = sqrt(2) CD " "or, 250= sqrt(2)CD`
or, ` CD = (250)/(sqrt(2)) = 125sqrt(2)` .
Hence in the first case the height of the kite is `125sqrt(3)` metres and in the second case the height of the kite is `125sqrt(2)` metres.
Clearly, the height of the kite is greater in the first case.