A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

Let the height of the tree be h meters.
Let the length of the broken part of the tree be x meters.
The broken part of the tree makes an angle of 30° with the ground.
The distance between the foot of the tree and the point where the top touches the ground is 8m.
From the right-angled triangle formed, we have:
cos(30°) = 8/x
x = 8/cos(30°)
x = 8/(√3/2)
x = 16/√3
Also, we have:
sin(30°) = (h-y)/x
where y is the height of the unbroken part of the tree.
1/2 = (h-y)/(16/√3)
h - y = 8/√3
In the right-angled triangle, we have:
x² = y² + 8²
(16/√3)² = y² + 64
256/3 = y² + 64
y² = 256/3 - 192/3
y² = 64/3
y = 8/√3
Then the height of the tree is:
h = y + 8/√3
h = 8/√3 + 8/√3
h = 16/√3
h = 16√3/3
h ≈ 9.24 meters
Therefore, the height of the tree is approximately 9.24 meters.