what is the approximate value of y − x?

x = 36.4 degrees

y = 53.6 degrees

y - x = 17.2 degrees

Step-by-step explanation:

Since we know the two short sides (legs) of a right angle triangle, we can use the tangent function to find one of the angles. For example for angle "y" we would have:

where the name "opp" indicates the side opposite angle y, while the name "adj" indicates the side adjacent to angle y.

We use the arct-tangent function to estimate angle y, and round it to one decimal:

Now that we know angle y, angle x can be obtained by using the property of internal angles of a triangle must add to 180. We also use that this is a right angle triangle, where we know one of the angles measure 90 degrees (the right angle). Therefore:

Angle x = 180 - 90 - 53.6 = 36.4 degrees

Now, we can calculate the difference of the two: y - x = 53.6 - 36.4 = 17.2 degrees.

c. 1,233 miles