Find the moon and sun diameter

Question

Diameters of the moon and the sun, viewed from Earth, both occupy about (1/2)° of the horizon. The distance to the moon is 390,000 km, and the distance to the sun is 150 million km. Find approximate diameters of the moon and the sun.

In the respective units, round the moon diameter to the nearest hundred and the sun diameter to one decimal place.

Moon diameter = ? km

Sun diameter =? million km

Hint given: the arc length s spanned by an angle of θ radians in a circle of radius r is given by s = rθ. You should take s as the diameter of the moon or sun.

Answer 1

Step 1 is to convert (¹/₂)° into radians: ¹/₂ ÷ 180 x π = (¹/₃₆₀)π radians

Step 2 is to plug this angle, and each of the radii (the distances to the moon and the sun) into the formula to determine the arc length (diameter of the moon and the sun)

Moon: s = (¹/₃₆₀)π x 390,000 km = 3,403.39 km ≅ 3,400 km

Sun: s = (¹/₃₆₀)π x 150 million km = 1.308997 million km ≅ 1.3 million km