The top of a tree is broken by a storm and the broken part touches the ground at a point 15 m from the base of the tree. If the tree is broken at a height of 8 m above the ground and the broken top remains attached, what was the original total height (in metres) of the tree?

Introduction:
This is a classic broken-tree (or broken-pole) trigonometry-style question, but it can be solved using only the Pythagoras theorem. The intact lower part of the tree remains vertical, while the broken top forms a right-angled triangle with the ground and the remaining vertical part.

Given Data / Assumptions:

• The tree is broken at a height of 8 m above the ground.
• The top of the broken part touches the ground at a point 15 m horizontally from the base.
• The broken top remains attached to the stump, forming a straight segment from the break point to the ground.
• The tree was vertical before breaking and the ground is level.

Concept / Approach:
We treat the situation as a right-angled triangle. The remaining vertical part of the tree is one leg of the triangle, the horizontal distance from the base to where the top touches the ground is the other leg, and the broken top itself forms the hypotenuse. Once the length of the broken part is found, we add it to the unbroken stump height to get the original height.

Step-by-Step Solution:
Step 1: Let the length of the broken top be L.Step 2: The vertical leg is 8 m (height of the break point).Step 3: The horizontal leg is 15 m (distance from base to where the top touches the ground).Step 4: Apply Pythagoras theorem: L² = 8² + 15².Step 5: Compute: 8² = 64 and 15² = 225, so L² = 64 + 225 = 289.Step 6: Take the square root: L = √289 = 17 m.Step 7: Original height of the tree = stump height + broken part length = 8 + 17 = 25 m.

Verification / Alternative check:
Check the triangle: sides 8, 15, and 17 form a well-known Pythagorean triple (8² + 15² = 17²). This confirms our triangle is right-angled and that 17 m is the correct length of the broken part, giving a total height of 25 m.

Why Other Options Are Wrong:
Heights like 17 m or 23 m account only for part of the tree, not both sections. Values like 27 m or 30 m are obtained if the Pythagoras theorem is misapplied or if 8 and 15 are incorrectly combined (for example, just adding them without considering the hypotenuse). They do not satisfy the right-triangle relationship.

Common Pitfalls:
A frequent mistake is to think that the original height is simply 15 + 8 = 23 m or to treat 15 m as the hypotenuse. Always identify which segment is slant (hypotenuse) and which are horizontal and vertical legs before applying Pythagoras theorem.

Final Answer:
The original height of the tree was 25 m.