Tree Shadow Height Calculation
This problem uses the concept of similar triangles or direct proportion. Since the sun's rays are parallel at a given time, the ratio of an object's height to its shadow's length remains constant.
Proportion Setup
Let $H_{person}$ be the height of the person and $S_{person}$ be the length of the person's shadow. Let $H_{tree}$ be the height of the tree and $S_{tree}$ be the length of the tree's shadow.
The proportion is set up as:
$ \frac{H_{person}}{S_{person}} = \frac{H_{tree}}{S_{tree}} $Applying Values
Given values are:
- Person's height ($H_{person}$): 5 feet
- Person's shadow ($S_{person}$): 4 feet
- Tree's shadow ($S_{tree}$): 20 feet
Substitute these into the proportion:
$ \frac{5 \text{ feet}}{4 \text{ feet}} = \frac{H_{tree}}{20 \text{ feet}} $Solving for Tree Height
To find the tree's height ($H_{tree}$), we solve the equation:
$ H_{tree} = \frac{5}{4} \times 20 \text{ feet} $Calculate the result:
$ H_{tree} = 5 \times \left(\frac{20}{4}\right) \text{ feet} $ $ H_{tree} = 5 \times 5 \text{ feet} $ $ H_{tree} = 25 \text{ feet} $Result
The height of the tree is 25 feet.
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?
