Question

A person looks at different trees in on open space with the following details. Arrange the trees in decreasing order of their apparent sizes.

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

Answer 1

The visual angles made by the tree with the eyes can be calculated as below

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

$=\frac{AB}{OB}$

$\Rightarrow {\theta }_A=\frac{2}{50}=\frac{1}{25}=0.04$

Similarly ${\theta }_B=\frac{2.5}{80}=0.02571$

$\Rightarrow {\theta }_C=\frac{1.8}{70}=0.0271$

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

Since ${\theta }_A>{\theta }_B>{\theta }_D>{\theta }_C$ the arrangement in decreasing order is given by A, B, D, and C