Step 1.
Calculate measure of angle α:
Step 2.
Calculate what fraction of the angle 360° is the angle α:
Step 3.
Calculate the circumference of the Earth (circle):
Step 4.
The length of arc is equal 1/40 of the circumference:
To find which ratio is higher, we can first convert the ratios into fractions (that makes it easier, at least for me) and then simplify the fractions and see which one is greater.
Since ratios are basically division, 15:20 = , and
12:16 =
Now we simplify these fractions. 15 and 20 have a GCF of 5, so taking out the common number gives us the simplified fraction of .
12 and 16 have a GCF of 4, so taking out the common number gives us the simplified fraction of . Since
=
, these ratios are the same.