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="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.