Taking the sum's distance as `1.4950xx10^(8)` km and the angle subtended by the sum at a point O on earth as half a degree, find approximately the diameter of the sun.

Answer

To find the diameter of the Sun based on the given information, we can follow these steps:

### Step 1: Understand the problem
We are given:
- Distance from the Earth to the Sun (D) = \(1.495 \times 10^8\) km
- Angle subtended by the Sun at point O on Earth (θ) = 0.5 degrees

We need to find the diameter of the Sun (d).

### Step 2: Convert the angle from degrees to radians
To use the formula for arc length, we need to convert the angle from degrees to radians. The conversion formula is:
\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \]
So, converting 0.5 degrees to radians:
\[ \theta = 0.5 \times \left(\frac{\pi}{180}\right) \approx 0.00872665 \text{ radians} \]

### Step 3: Use the arc length formula
The arc length (s) can be calculated using the formula:
\[ s = D \times \theta \]
Where:
- \(s\) is the arc length (which is the diameter of the Sun in this case)
- \(D\) is the distance from the Earth to the Sun
- \(\theta\) is the angle in radians

Substituting the values:
\[ s = 1.495 \times 10^8 \times 0.00872665 \]

### Step 4: Calculate the arc length
Now we perform the multiplication:
\[ s \approx 1.495 \times 10^8 \times 0.00872665 \approx 1.304 \times 10^6 \text{ km} \]

### Step 5: Relate arc length to diameter
Since the arc length we calculated is actually the diameter of the Sun, we can conclude:
\[ d \approx 1.304 \times 10^6 \text{ km} \]

### Final Answer
The approximate diameter of the Sun is \(1.304 \times 10^6\) km.

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