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.

$\begin{array}{ccc}\text{Tree}& \text{Height(m)}& \text{Distance from the eye(m)}\\ \text{A}& 2.0& 50\\ \text{B}& 2.5& 80\\ \text{C}& 1.8& 70\\ \text{D}& 2.8& 100\end{array}$

• A. $A>B>C>D$
• B. $A>B>D>C$
• C. $B>D>A>C$
• D. $D>B>C>D$

Answer 1

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:

$\tan \theta =\frac{\text{Height of the tree}}{\text{Distance from the eyes}}$

$\Rightarrow \tan \theta =\frac{AB}{OB}$


For tree $A$:

$\tan {\theta }_A=\frac{2}{50}=0.04$

For tree $B$:

$\tan {\theta }_B=\frac{2.5}{80}=0.03225$

For tree $C$:

$\tan {\theta }_C=\frac{1.8}{70}=0.0257$

For tree $D$:

$\tan {\theta }_D=\frac{2.8}{100}=0.028$

Therefore, the decreasing order of their apparent size is:

$A>B>D>C$

Hence, $\left(B\right)$ is the correct answer.

Key Note: Visual angle is the measure of the apparent size of the objects.