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
If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two values which are in the ratio 1 : 3
2. x can be equal to the height of the flagstaff
Which of the statements given above is/are correct?
What is a possible value of tan θ ?
A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower?
Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15° with the horizontal. The distance between the poles is approximately equal to
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?
