Since the sun is very far away, the rays from the sun will be almost parallel to both the earth and the sun. So this means the angle of rays between the sun and the moon will be very small. Given the moon is perpendicular to the earth, we have 90 deg on that angle. Since the angles of a triangle add up to 180 deg, the remaining angle is very close to 90 deg, so 89.5 is a good approximation. (It could be 89.8 or 89.7) The result will be similar.

## how can we know it is 89.5

Since the sun is very far away, the rays from the sun will be almost parallel to both the earth and the sun. So this means the angle of rays between the sun and the moon will be very small. Given the moon is perpendicular to the earth, we have 90 deg on that angle. Since the angles of a triangle add up to 180 deg, the remaining angle is very close to 90 deg, so 89.5 is a good approximation. (It could be 89.8 or 89.7) The result will be similar.