Answer:
6.3 × 10⁶ square miles
Step-by-step explanation:
We are given,
The radius of the moon is approximately 1000 miles.
We know that the moon resembles a sphere and also,
Area of sphere = , where r is the radius.
Now, the area of the moon = = 1.26 × 10⁷ square miles
Since, only the half of the area is clear to view.
So, the area left to view = = 6.3 × 10⁶ square miles.
Hence, the area of the moon in view is 6.3 × 10⁶ square miles.
Look at the attached figure. We define the unit circle as a circle with center in the origin (0,0) and radius 1.
Then, we consider a point P on the circumference. We call the angle between the positive half of the x axis and the radius AP.
We define
As you can see, ACD is a right triangle, and so we have
But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that
