Answer:
1100 km
Explanation:
The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface. Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.
Draw circle representing the moon and earth. Draw tangent lines from the earth's center to the edge of the moon. The angle between these lines is the subtended angle. Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects. Notice this forms a right angle.
(See attached diagram)
Using trigonometry:
sin(θ/2) = r / (R + h)
r = (R + h) sin(θ/2)
Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:
r = (6400 + 380000) sin(1/6 °)
r = 1100
The moon's radius is 1100 km.