A person looks at different trees in an open space with the following details. Arrange the trees in

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.

Professor PC Thomas Classes · Answer

The apparent size of an object depends on the visual angle it subtends at the observer's eye. For small angles, the visual angle $	heta$ is approximately equal to the ratio of the height of the object ( $h$ ) to its distance from the eye ( $d$ ). 
$ 	heta \approx \frac{h}{d} $
Let's calculate the ratio for each tree: - Tree A: $	heta_A=\frac{2.0}{50}=0.040$ - Tree B: $	heta_B=\frac{2.5}{80}=0.03125$ - Tree C: $	heta_C=\frac{1.8}{70} \approx 0.0257$ - Tree D: $	heta_D=\frac{2.8}{100}=0.028$ Comparing the values: $0.040>0.03125>0.028>0.0257$. Therefore, the decreasing order of their apparent sizes is $\mathbf{A}>\mathbf{B}>\mathbf{D}>\mathbf{C}$.