Question

Assuming that a person with normal sight can read texts from such a distance that the letters subtend an angle of ${12}^{\prime }$ at his eye. What should be the height (in $cm$) of the letters that he can read from a distance of $7\text{m}$

• A. 2.44

Answer 1

The correct option is A 2.44
Let $h$ be the height of the letter.
The situation can be seen as:

Now, we know the length of the arc as: $l=\frac{\alpha }{{360}^{\circ }}\times 2\pi \times r$
here $h=l,r=7\text{m}\&\alpha ={12}^{\prime }=\frac{{12}^{\circ }}{60}$
Now, substituting the value in the equation, we get:

$h=\frac{{12}^{\circ }}{60\times {360}^{\circ }}\times 2\pi \times 7\text{m}$

$\Rightarrow h=\frac{1}{5\times 360}\times 2\pi \times 700\text{cm}\approx 2.44\text{cm}$

Hence, the height of the text should be $2.44\text{cm}$ for the person able to read the text.