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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.
| Tree | Height(m) | Distance from the eye(m) |
| A | 2.0 | 50 |
| B | 2.5 | 80 |
| C | 1.8 | 70 |
| D | 2.8 | 100 |
Solution
Let the tree make a visual angle θ with the eyes.
Thus, we have:
`theta="Height of the tree"/"Distance from the eye"`
For tree A ,`theta_A =2/50 =0.04`
For tree B, `theta_B =2.5/80 =0.03125`
For tree C , `theta_C = 1.8/70 = 0.0257`
For tree D , `theta_D = 2.8/100 = 0.028`
Now,
`theta_A> theta_B>theta_D>theta_C`
The more the value of θ, the bigger the apparent size of the tree.
So, the arrangement in decreasing order is A, B, D and C.
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