Tree Height Calculation Using Pythagorean Theorem
The problem describes a scenario that can be modeled using a right-angled triangle.
- The height at which the tree broke forms one leg of the triangle (let's call it a).
- The distance from the foot of the tree to where the broken part touches the ground forms the other leg (let's call it b).
- The broken upper part of the tree forms the hypotenuse (let's call it c).
Given values:
- Standing part of the tree, a = 8 m
- Distance on the ground, b = 6 m
Finding the Broken Part Length
We use the Pythagorean theorem to find the length of the broken part (hypotenuse, c):
$ a^2 + b^2 = c^2 $
Substitute the given values:
$ 8^2 + 6^2 = c^2 $
$ 64 + 36 = c^2 $
$ 100 = c^2 $
Solve for c:
$ c = \sqrt{100} $
$ c = 10 \text{ m} $
So, the length of the broken upper part is 10 m.
Calculating Total Tree Height
The total height of the tree is the sum of the standing part and the broken part.
Total Height = Standing Part (a) + Broken Part (c)
Total Height = 8 m + 10 m
Total Height = 18 m
The height of the tree is 18 m.
Similar Questions
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Important Questions from Heights and Distances
A peacock sitting at the top of a 3 meter high pole saw a snake approaching towards pole at a distance three times of the height of the pole. Then it jumping from pole will catch the snake at what distance from the pole if both are running with same speed ?
The foot of a ladder 25 m long is 7 m from the base of the building. If the top of the ladder slips by 4 m, then by how much distance will the foot of the ladder slide?
Two hotels stand 25 m apart. One of them is 70 m high and the angle of depression of the top of other as observed from the top of this hotel is 45°. Height of the other hotel is:
If the angles of elevation of a balloon from two consecutive kilometer-stones along a straight road are 30° and 60° respectively, then the height of the balloon above the ground will be:
The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?
