advanced functions
posted by Anonymous on .
The Moon has a diameter of about 3480 km and an orbital radius of about 384 400 km from the centre of Earth. Suppose that the Moon is directly overhead. What is the measure of the angle subtended by the diameter to the Moon as measured by an astronomer on the surface of Earth? Answer in both radians and degrees.

Diameter of the moon = 3480 km
Distance from surface of the earth
= Distance to centre  radius of the earth
= 3844006400 km
= 378000 km
Since the angle is very small, we can approximate the arclength by the chord length, equal to the diameter.
Angle subtended
= 3480/378000
= 0.0092 radian
If we had used the chord instead, the difference in angle calculated would have been 0.0000000325 radians more.
i.e.
angle
= 2*sin^{1}(1740/37800)
= 0.0092 radian 
Sorry, I actually have a question. According to the question that was posted. If I were to solve this question, without knowing the radius of the earth before hand. Is there any other solution??