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Question

A person looks at different trees in an open space with the following details. Arrange the trees in decreasing order of their apparent sizes.

TreeHeight(m)Distance from the eye(m)A2.050B2.580C1.870D2.8100

A
A>B>C>D
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B
A>B>D>C
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C
B>D>A>C
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D
D>B>C>D
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Solution

The correct option is B A>B>D>C
The visual angle is the measure of the apparent size of the objects.

The visual angle made by the tree with the eyes can be calculated as:

tanθ=Height of the treeDistance from the eyes

tanθ=ABOB


For tree A:

tanθA=250=0.04

For tree B:

tanθB=2.580=0.03225

For tree C:

tanθC=1.870=0.0257

For tree D:

tanθD=2.8100=0.028

Therefore, the decreasing order of their apparent size is:

A>B>D>C

Hence, (B) is the correct answer.
Key Note: Visual angle is the measure of the apparent size of the objects.

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