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

Answer 1

Let the tree make a visual angle θ with the eyes.
Thus, we have:
$\theta =\frac{\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{tree}}{\mathrm{Distance}\mathrm{from}\mathrm{the}\mathrm{eye}}$
For tree A, ${\theta }_{\mathrm{A}}=\frac{2}{50}=0.04$

For tree B, ${\theta }_{\mathrm{B}}=\frac{2.5}{80}=0.03125$

For tree C, ${\theta }_{\mathrm{C}}=\frac{1.8}{70}=0.0257$

For tree D, ${\theta }_{\mathrm{D}}=\frac{2.8}{100}=0.028$
Now,
θ_A > θ_B > θ_D > θ_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.