Question

 the lower window of the house is ata height of 2 metre above the groundand its upper window is 4 metre vertically above the lower windo. at certain instant the angles of alevation of the balloon from these windows are observed to be 60degree and 30 degree respectively.find the height of balloon above the ground

Answer 1

Let the height of balloon from ground = y
horizontal distance between window and balloon = x
(see picture)

tan 30 = (y-6)x
⇒1/√3 = (y-6)/x
⇒x = √3 × (y-6)

tan 60 = (y-2)/x
⇒√3 = (y-2)/x
⇒ x = (y-2)/√3

So √3 × (y-6) = (y-2)/√3
⇒ 3(y-6) = y-2
⇒3y - 18 = y - 2
⇒ 3y - y = -2 +18
⇒2y = 16
⇒ y = 16/2 = 8 m

Height of balloon above ground is 8m.