Answer:
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: [tex]tan(y)=\frac{opp}{adj} =\frac{19.1}{14.1}[/tex]
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:
[tex]tan(y)=\frac{opp}{adj} =\frac{19.1}{14.1}\\y=arctan(\frac{19.1}{14.1})=53.6^o[/tex]
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.
