Assuming that a person of normal sight can read print at such a distance that the letters subtend an angle of 5' at his eye. Find what is the height of the letters that he can read at a distance of 756 meteres ?

Answer

To solve the problem, we need to determine the height of the letters that a person can read at a distance of 756 meters, given that the letters subtend an angle of 5 minutes at the person's eye.

### Step-by-Step Solution:

1. **Understanding the Angle**:
The angle subtended by the letters at the eye is given as 5 minutes. We need to convert this angle into radians for our calculations.

\[ \text{Angle in degrees} = \frac{5}{60} \text{ degrees} \]

2. **Convert Degrees to Radians**:
To convert degrees to radians, we use the conversion factor \(\frac{\pi}{180}\).

\[ \text{Angle in radians} = \frac{5}{60} \times \frac{\pi}{180} = \frac{5\pi}{10800} \text{ radians} \]

3. **Using the Formula**:
The relationship between the height of the letters (L), the distance from the eye (R), and the angle (θ) is given by the formula:

\[ L = R \cdot \theta \]

Here, \(R = 756\) meters and \(\theta = \frac{5\pi}{10800}\) radians.

4. **Substituting the Values**:
Now we substitute the values into the formula:

\[ L = 756 \cdot \frac{5\pi}{10800} \]

5. **Simplifying the Expression**:
We can simplify this expression step by step:

- First, calculate \(756 \cdot 5 = 3780\).
- Now, substitute this back into the equation:

\[ L = \frac{3780\pi}{10800} \]

- Simplifying \(\frac{3780}{10800}\):

\[ L = \frac{3780 \div 3780}{10800 \div 3780} \cdot \pi = \frac{1}{2.857} \cdot \pi \approx \frac{1}{3.5} \cdot \pi \approx 1.1 \text{ meters} \]

6. **Final Answer**:
Thus, the height of the letters that can be read at a distance of 756 meters is approximately:

\[ L \approx 1.1 \text{ meters} \]