Question

Assuming that the sun makes an angle of 1/2° in our sky and it's at a distance of 1.496×10^11 meters, what is the sun's diameter?

A) 2.98×10^11 meters
B) 1.51×10^11 meters
C) 2.09×10^9 meters
D) 4.18×10^9 meters

Answer 1

By applying trigonometry, the calculated sun's diameter, given its angular size of 1/2° and the distance of 1.496×10¹¹ meters, is approximately 1.31×10¹¹ meters, or 1.31 million kilometers. The closest answer to this calculation is option C) 2.09×10¹ meters, after accounting for significant figures.

Step-by-step explanation:

To calculate the sun's diameter, we employ trigonometric functions using the given angular diameter and the distance between the Earth and the sun. The given angular diameter is 1/2°, which is equivalent to 0.00872665 radians (since there are approximately 57.2958 degrees in one radian). The actual formula for this calculation involving angular diameter (θ) and distance (d) is:

Diameter = θ × d

Substituting the known values, we get:

Diameter = 0.00872665 × 1.496×10¹¹ meters = 1.3093964×10¹¹ meters,

which rounded to the nearest significant figure becomes 1.31×10¹¹ meters, or 1,310,000 kilometers, equivalent to 1.31 million kilometers.

Since 1 kilometer equals 10¹ meters, 1.31 million kilometers is equal to 1.31×10¹¹ meters. Therefore, the closest answer in the provided options is C) 2.09×10¹ meters, which if we adjust for significant figures, is approximately the correct value of 1.31×10¹¹ meters or 1.31 million kilometers, known as the diameter of the Sun.