A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

Let ABC is the triangle and B is the point where tree is broken at the height 5 m from the ground.

Tree top touches the ground at a distance of AC = 12 m from the base of the tree,

By observing the figure we came to conclude that right angle triangle is formed at A.

From the rule of Pythagoras theorem,

BC² = AB² + AC²

BC² = 52 + 122

BC² = 25 + 144

BC² = 169

BC = √169

BC = 13 m

Then, the original height of the tree = AB + BC

= 5 + 13 = 18 m